A rational finite element basis /:
A rational finite element basis.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York :
Academic Press,
1975.
|
| Schriftenreihe: | Mathematics in science and engineering ;
v. 114. |
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Zusammenfassung: | A rational finite element basis. |
| Beschreibung: | 1 online resource (xiii, 331 pages) |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliographie: | Includes bibliographical references (pages 322-325) and index. |
| ISBN: | 9780127289502 012728950X 9780080956237 0080956238 128229010X 9781282290105 |
Internformat
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn316568480 | ||
| 003 | OCoLC | ||
| 005 | 20241004212047.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 090320s1975 nyu ob 001 0 eng d | ||
| 040 | |a OPELS |b eng |e pn |c OPELS |d N$T |d OCLCQ |d EBLCP |d IDEBK |d OPELS |d E7B |d OCLCQ |d OPELS |d OCLCQ |d OCLCF |d OCLCE |d DEBBG |d OCLCQ |d NLGGC |d OCLCQ |d COO |d OCLCQ |d DEBSZ |d KIJ |d AGLDB |d OCLCQ |d MERUC |d OCLCQ |d VTS |d OCLCQ |d STF |d K6U |d OCLCQ |d LUN |d AJS |d OCLCQ |d OCLCO |d SGP |d OCLCQ |d OCLCO |d OCLCL | ||
| 019 | |a 609173887 |a 646827863 |a 757401120 |a 823843595 |a 823912337 |a 824099366 |a 824154788 |a 978532340 |a 978904931 |a 1027284680 |a 1047884879 |a 1086556974 |a 1157103821 |a 1157994633 |a 1178674172 |a 1183904065 | ||
| 020 | |a 9780127289502 |q (electronic bk.) | ||
| 020 | |a 012728950X |q (electronic bk.) | ||
| 020 | |a 9780080956237 |q (electronic bk.) | ||
| 020 | |a 0080956238 |q (electronic bk.) | ||
| 020 | |a 128229010X | ||
| 020 | |a 9781282290105 | ||
| 035 | |a (OCoLC)316568480 |z (OCoLC)609173887 |z (OCoLC)646827863 |z (OCoLC)757401120 |z (OCoLC)823843595 |z (OCoLC)823912337 |z (OCoLC)824099366 |z (OCoLC)824154788 |z (OCoLC)978532340 |z (OCoLC)978904931 |z (OCoLC)1027284680 |z (OCoLC)1047884879 |z (OCoLC)1086556974 |z (OCoLC)1157103821 |z (OCoLC)1157994633 |z (OCoLC)1178674172 |z (OCoLC)1183904065 | ||
| 042 | |a dlr | ||
| 050 | 4 | |a TA347.F5 |b W33 1975eb | |
| 072 | 7 | |a MAT |x 007020 |2 bisacsh | |
| 072 | 7 | |a GPF |2 bicssc | |
| 082 | 7 | |a 515.3/53 |2 22 | |
| 084 | |a 50.04 |2 bcl | ||
| 049 | |a MAIN | ||
| 100 | 1 | |a Wachspress, Eugene L. | |
| 245 | 1 | 2 | |a A rational finite element basis / |c Eugene L. Wachspress. |
| 260 | |a New York : |b Academic Press, |c 1975. | ||
| 300 | |a 1 online resource (xiii, 331 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Mathematics in science and engineering ; |v v. 114 | |
| 504 | |a Includes bibliographical references (pages 322-325) and index. | ||
| 588 | 0 | |a Print version record. | |
| 506 | |3 Use copy |f Restrictions unspecified |2 star |5 MiAaHDL | ||
| 520 | |a A rational finite element basis. | ||
| 533 | |a Electronic reproduction. |b [Place of publication not identified] : |c HathiTrust Digital Library, |d 2010. |5 MiAaHDL | ||
| 538 | |a Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |u http://purl.oclc.org/DLF/benchrepro0212 |5 MiAaHDL | ||
| 583 | 1 | |a digitized |c 2010 |h HathiTrust Digital Library |l committed to preserve |2 pda |5 MiAaHDL | |
| 505 | 0 | |a Front Cover; A Rational Finite Element Basis; Copyright Page; CONTENTS; PREFACE; THEOREMS AND LEMMAS; Chapter 1. PATCHWORK APPROXIMATION IN NUMERICAL ANALYSIS; 1.1 Wedges and Pyramids; 1.2 Definitions and Notation; 1.3 Continuity; 1.4 Patchwork Approximation Spaces and Convergence; 1.5 Wedge Properties; 1.6 Isoparametric Coordinates; 1.7 Generalizations to Sides of Higher Order and to Three-Dimensional Elements; 1.8 Remarks and References; Chapter 2. THE QUADRILATERAL; 2.1 Inadequacy of Polynomials; 2.2 Rational Wedges; 2.3 Areal Coordinates as Limits of Rational Wedges | |
| 505 | 8 | |a 2.4 An Example of Quadrilateral Wedges2.5 Projective Coordinates; 2.6 Polygons?; Chapter 3. RATIONAL WEDGES FOR SELECTED POLYCONS; 3.1 The 3-Con of Order Four; 3.2 The 4-Con of Order Five; 3.3 The Pentagon; 3.4 Some Elementary Congruences; 3.5 Wedges for 3-Cons of Orders Five and Six; 3.6 Two-sided Elements; 3.7 Related Studies; Chapter 4. ALGEBRAIC GEOMETRY FOUNDATIONS; 4.1 Motivation; 4.2 Homogeneous Coordinates and the Projective Plane; 4.3 Intersection of Plane Curves; 4.4 The Fundamental Congruence Theorem; 4.5 Associated Points; 4.6 Resolution of Singularities | |
| 505 | 8 | |a 4.7 Remarks and ReferencesChapter 5. RATIONAL WEDGE CONSTRUCTION FOR POLYCONS AND POLYPOLS; 5.1 Polycon Wedge Construction; 5.2 Verification of Polycon Wedge Properties; 5.3 The Case of the Vanishing Denominator; 5.4 Polypols and Deficit Intersection Points; 5.5 Polypol Wedge Numerators and Adjunct Intersection Points; 5.6 Illustrative Polycubes; Chapter 6. APPROXIMATION OF HIGHER DEGREE; 6.1 Data Fitting; 6.2 Degree Two Approximation; 6.3 Degree Three and Higher Degree Approximation; 6.4 Intermediate Approximation; 6.5 Higher Degree Approximation on Polypols | |
| 505 | 8 | |a 6.6 A Concise Algebraic Geometry Analysis6.7 Algebrais Reticulation; Chapter 7. THREE-DIMENSIONAL APPROXIMATION; 7.1 Definitions and Background; 7.2 Triangular Prisms and Hexahedra; 7.3 Polyhedra; 7.4 Polycondra; 7.5 The Adjoint of a Well-Set Polypoldron; 7.6 Polypoldra Nodes and Adjacent Factors for Degree k Approximation; 7.7 Attainment of Degree k Approximation; Chapter 8. A RATIONAL SOLUTION TO AN IRRATIONAL PROBLEM; 8.1 Irrational Wedges; 8.2 The Method of Descent; 8.3 Wedges for an Ill-Set Polycon; 8.4 Nonconvex Quadrilaterals; 8.5 Remarks; Chapter 9. FINITE ELEMENT DISCRETIZATION | |
| 505 | 8 | |a 9.1 Introductory Remarks9.2 Some Simple Quadrature Formulas; 9.3 Consistent Quadrature and the Patch Test; 9.4 Triangle Averaging; 9.5 Mosaic Discretization; 9.6 A Discrete Laplacian for Quadrilaterals; 9.7 Harmonious Discretization; Chapter 10. TWO-LEVEL COMPUTATION; 10.1 Recapitulation; 10.2 Synthesis; 10.3 Coarse Mesh Rebalancing; 10.4 Concluding Remarks; REFERENCES; INDEX | |
| 650 | 0 | |a Finite element method. |0 http://id.loc.gov/authorities/subjects/sh85048349 | |
| 650 | 6 | |a Méthode des éléments finis. | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x Partial. |2 bisacsh | |
| 650 | 7 | |a Finite element method |2 fast | |
| 758 | |i has work: |a A Rational finite element basis (Text) |1 https://id.oclc.org/worldcat/entity/E39PCXCmFyk6tfQ4rGJY7cBWym |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Wachspress, Eugene L. |t Rational finite element basis. |d New York : Academic Press, 1975 |z 9780127289502 |w (DLC) 75012594 |w (OCoLC)1324549 |
| 830 | 0 | |a Mathematics in science and engineering ; |v v. 114. |0 http://id.loc.gov/authorities/names/n42015986 | |
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=297165 |3 Volltext |
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://www.sciencedirect.com/science/bookseries/00765392/114 |3 Volltext |
| 938 | |a EBL - Ebook Library |b EBLB |n EBL453170 | ||
| 938 | |a ebrary |b EBRY |n ebr10329612 | ||
| 938 | |a EBSCOhost |b EBSC |n 297165 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n 229010 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn316568480 |
|---|---|
| _version_ | 1816881689331236864 |
| adam_text | |
| any_adam_object | |
| author | Wachspress, Eugene L. |
| author_facet | Wachspress, Eugene L. |
| author_role | |
| author_sort | Wachspress, Eugene L. |
| author_variant | e l w el elw |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | T - Technology |
| callnumber-label | TA347 |
| callnumber-raw | TA347.F5 W33 1975eb |
| callnumber-search | TA347.F5 W33 1975eb |
| callnumber-sort | TA 3347 F5 W33 41975EB |
| callnumber-subject | TA - General and Civil Engineering |
| collection | ZDB-4-EBA |
| contents | Front Cover; A Rational Finite Element Basis; Copyright Page; CONTENTS; PREFACE; THEOREMS AND LEMMAS; Chapter 1. PATCHWORK APPROXIMATION IN NUMERICAL ANALYSIS; 1.1 Wedges and Pyramids; 1.2 Definitions and Notation; 1.3 Continuity; 1.4 Patchwork Approximation Spaces and Convergence; 1.5 Wedge Properties; 1.6 Isoparametric Coordinates; 1.7 Generalizations to Sides of Higher Order and to Three-Dimensional Elements; 1.8 Remarks and References; Chapter 2. THE QUADRILATERAL; 2.1 Inadequacy of Polynomials; 2.2 Rational Wedges; 2.3 Areal Coordinates as Limits of Rational Wedges 2.4 An Example of Quadrilateral Wedges2.5 Projective Coordinates; 2.6 Polygons?; Chapter 3. RATIONAL WEDGES FOR SELECTED POLYCONS; 3.1 The 3-Con of Order Four; 3.2 The 4-Con of Order Five; 3.3 The Pentagon; 3.4 Some Elementary Congruences; 3.5 Wedges for 3-Cons of Orders Five and Six; 3.6 Two-sided Elements; 3.7 Related Studies; Chapter 4. ALGEBRAIC GEOMETRY FOUNDATIONS; 4.1 Motivation; 4.2 Homogeneous Coordinates and the Projective Plane; 4.3 Intersection of Plane Curves; 4.4 The Fundamental Congruence Theorem; 4.5 Associated Points; 4.6 Resolution of Singularities 4.7 Remarks and ReferencesChapter 5. RATIONAL WEDGE CONSTRUCTION FOR POLYCONS AND POLYPOLS; 5.1 Polycon Wedge Construction; 5.2 Verification of Polycon Wedge Properties; 5.3 The Case of the Vanishing Denominator; 5.4 Polypols and Deficit Intersection Points; 5.5 Polypol Wedge Numerators and Adjunct Intersection Points; 5.6 Illustrative Polycubes; Chapter 6. APPROXIMATION OF HIGHER DEGREE; 6.1 Data Fitting; 6.2 Degree Two Approximation; 6.3 Degree Three and Higher Degree Approximation; 6.4 Intermediate Approximation; 6.5 Higher Degree Approximation on Polypols 6.6 A Concise Algebraic Geometry Analysis6.7 Algebrais Reticulation; Chapter 7. THREE-DIMENSIONAL APPROXIMATION; 7.1 Definitions and Background; 7.2 Triangular Prisms and Hexahedra; 7.3 Polyhedra; 7.4 Polycondra; 7.5 The Adjoint of a Well-Set Polypoldron; 7.6 Polypoldra Nodes and Adjacent Factors for Degree k Approximation; 7.7 Attainment of Degree k Approximation; Chapter 8. A RATIONAL SOLUTION TO AN IRRATIONAL PROBLEM; 8.1 Irrational Wedges; 8.2 The Method of Descent; 8.3 Wedges for an Ill-Set Polycon; 8.4 Nonconvex Quadrilaterals; 8.5 Remarks; Chapter 9. FINITE ELEMENT DISCRETIZATION 9.1 Introductory Remarks9.2 Some Simple Quadrature Formulas; 9.3 Consistent Quadrature and the Patch Test; 9.4 Triangle Averaging; 9.5 Mosaic Discretization; 9.6 A Discrete Laplacian for Quadrilaterals; 9.7 Harmonious Discretization; Chapter 10. TWO-LEVEL COMPUTATION; 10.1 Recapitulation; 10.2 Synthesis; 10.3 Coarse Mesh Rebalancing; 10.4 Concluding Remarks; REFERENCES; INDEX |
| ctrlnum | (OCoLC)316568480 |
| dewey-full | 515.3/53 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3/53 |
| dewey-search | 515.3/53 |
| dewey-sort | 3515.3 253 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>06449cam a2200697 a 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn316568480</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20241004212047.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr cnu---unuuu</controlfield><controlfield tag="008">090320s1975 nyu ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">OPELS</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">OPELS</subfield><subfield code="d">N$T</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">EBLCP</subfield><subfield code="d">IDEBK</subfield><subfield code="d">OPELS</subfield><subfield code="d">E7B</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OPELS</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCF</subfield><subfield code="d">OCLCE</subfield><subfield code="d">DEBBG</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">NLGGC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">COO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">DEBSZ</subfield><subfield code="d">KIJ</subfield><subfield code="d">AGLDB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">MERUC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">VTS</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">STF</subfield><subfield code="d">K6U</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">LUN</subfield><subfield code="d">AJS</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">SGP</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">609173887</subfield><subfield code="a">646827863</subfield><subfield code="a">757401120</subfield><subfield code="a">823843595</subfield><subfield code="a">823912337</subfield><subfield code="a">824099366</subfield><subfield code="a">824154788</subfield><subfield code="a">978532340</subfield><subfield code="a">978904931</subfield><subfield code="a">1027284680</subfield><subfield code="a">1047884879</subfield><subfield code="a">1086556974</subfield><subfield code="a">1157103821</subfield><subfield code="a">1157994633</subfield><subfield code="a">1178674172</subfield><subfield code="a">1183904065</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780127289502</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">012728950X</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780080956237</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0080956238</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">128229010X</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781282290105</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)316568480</subfield><subfield code="z">(OCoLC)609173887</subfield><subfield code="z">(OCoLC)646827863</subfield><subfield code="z">(OCoLC)757401120</subfield><subfield code="z">(OCoLC)823843595</subfield><subfield code="z">(OCoLC)823912337</subfield><subfield code="z">(OCoLC)824099366</subfield><subfield code="z">(OCoLC)824154788</subfield><subfield code="z">(OCoLC)978532340</subfield><subfield code="z">(OCoLC)978904931</subfield><subfield code="z">(OCoLC)1027284680</subfield><subfield code="z">(OCoLC)1047884879</subfield><subfield code="z">(OCoLC)1086556974</subfield><subfield code="z">(OCoLC)1157103821</subfield><subfield code="z">(OCoLC)1157994633</subfield><subfield code="z">(OCoLC)1178674172</subfield><subfield code="z">(OCoLC)1183904065</subfield></datafield><datafield tag="042" ind1=" " ind2=" "><subfield code="a">dlr</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">TA347.F5</subfield><subfield code="b">W33 1975eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">007020</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">GPF</subfield><subfield code="2">bicssc</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">515.3/53</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">50.04</subfield><subfield code="2">bcl</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Wachspress, Eugene L.</subfield></datafield><datafield tag="245" ind1="1" ind2="2"><subfield code="a">A rational finite element basis /</subfield><subfield code="c">Eugene L. Wachspress.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">New York :</subfield><subfield code="b">Academic Press,</subfield><subfield code="c">1975.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xiii, 331 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Mathematics in science and engineering ;</subfield><subfield code="v">v. 114</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 322-325) and index.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="506" ind1=" " ind2=" "><subfield code="3">Use copy</subfield><subfield code="f">Restrictions unspecified</subfield><subfield code="2">star</subfield><subfield code="5">MiAaHDL</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">A rational finite element basis.</subfield></datafield><datafield tag="533" ind1=" " ind2=" "><subfield code="a">Electronic reproduction.</subfield><subfield code="b">[Place of publication not identified] :</subfield><subfield code="c">HathiTrust Digital Library,</subfield><subfield code="d">2010.</subfield><subfield code="5">MiAaHDL</subfield></datafield><datafield tag="538" ind1=" " ind2=" "><subfield code="a">Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.</subfield><subfield code="u">http://purl.oclc.org/DLF/benchrepro0212</subfield><subfield code="5">MiAaHDL</subfield></datafield><datafield tag="583" ind1="1" ind2=" "><subfield code="a">digitized</subfield><subfield code="c">2010</subfield><subfield code="h">HathiTrust Digital Library</subfield><subfield code="l">committed to preserve</subfield><subfield code="2">pda</subfield><subfield code="5">MiAaHDL</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Front Cover; A Rational Finite Element Basis; Copyright Page; CONTENTS; PREFACE; THEOREMS AND LEMMAS; Chapter 1. PATCHWORK APPROXIMATION IN NUMERICAL ANALYSIS; 1.1 Wedges and Pyramids; 1.2 Definitions and Notation; 1.3 Continuity; 1.4 Patchwork Approximation Spaces and Convergence; 1.5 Wedge Properties; 1.6 Isoparametric Coordinates; 1.7 Generalizations to Sides of Higher Order and to Three-Dimensional Elements; 1.8 Remarks and References; Chapter 2. THE QUADRILATERAL; 2.1 Inadequacy of Polynomials; 2.2 Rational Wedges; 2.3 Areal Coordinates as Limits of Rational Wedges</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">2.4 An Example of Quadrilateral Wedges2.5 Projective Coordinates; 2.6 Polygons?; Chapter 3. RATIONAL WEDGES FOR SELECTED POLYCONS; 3.1 The 3-Con of Order Four; 3.2 The 4-Con of Order Five; 3.3 The Pentagon; 3.4 Some Elementary Congruences; 3.5 Wedges for 3-Cons of Orders Five and Six; 3.6 Two-sided Elements; 3.7 Related Studies; Chapter 4. ALGEBRAIC GEOMETRY FOUNDATIONS; 4.1 Motivation; 4.2 Homogeneous Coordinates and the Projective Plane; 4.3 Intersection of Plane Curves; 4.4 The Fundamental Congruence Theorem; 4.5 Associated Points; 4.6 Resolution of Singularities</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">4.7 Remarks and ReferencesChapter 5. RATIONAL WEDGE CONSTRUCTION FOR POLYCONS AND POLYPOLS; 5.1 Polycon Wedge Construction; 5.2 Verification of Polycon Wedge Properties; 5.3 The Case of the Vanishing Denominator; 5.4 Polypols and Deficit Intersection Points; 5.5 Polypol Wedge Numerators and Adjunct Intersection Points; 5.6 Illustrative Polycubes; Chapter 6. APPROXIMATION OF HIGHER DEGREE; 6.1 Data Fitting; 6.2 Degree Two Approximation; 6.3 Degree Three and Higher Degree Approximation; 6.4 Intermediate Approximation; 6.5 Higher Degree Approximation on Polypols</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">6.6 A Concise Algebraic Geometry Analysis6.7 Algebrais Reticulation; Chapter 7. THREE-DIMENSIONAL APPROXIMATION; 7.1 Definitions and Background; 7.2 Triangular Prisms and Hexahedra; 7.3 Polyhedra; 7.4 Polycondra; 7.5 The Adjoint of a Well-Set Polypoldron; 7.6 Polypoldra Nodes and Adjacent Factors for Degree k Approximation; 7.7 Attainment of Degree k Approximation; Chapter 8. A RATIONAL SOLUTION TO AN IRRATIONAL PROBLEM; 8.1 Irrational Wedges; 8.2 The Method of Descent; 8.3 Wedges for an Ill-Set Polycon; 8.4 Nonconvex Quadrilaterals; 8.5 Remarks; Chapter 9. FINITE ELEMENT DISCRETIZATION</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">9.1 Introductory Remarks9.2 Some Simple Quadrature Formulas; 9.3 Consistent Quadrature and the Patch Test; 9.4 Triangle Averaging; 9.5 Mosaic Discretization; 9.6 A Discrete Laplacian for Quadrilaterals; 9.7 Harmonious Discretization; Chapter 10. TWO-LEVEL COMPUTATION; 10.1 Recapitulation; 10.2 Synthesis; 10.3 Coarse Mesh Rebalancing; 10.4 Concluding Remarks; REFERENCES; INDEX</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Finite element method.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85048349</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Méthode des éléments finis.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Differential Equations</subfield><subfield code="x">Partial.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Finite element method</subfield><subfield code="2">fast</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">A Rational finite element basis (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCXCmFyk6tfQ4rGJY7cBWym</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Wachspress, Eugene L.</subfield><subfield code="t">Rational finite element basis.</subfield><subfield code="d">New York : Academic Press, 1975</subfield><subfield code="z">9780127289502</subfield><subfield code="w">(DLC) 75012594</subfield><subfield code="w">(OCoLC)1324549</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Mathematics in science and engineering ;</subfield><subfield code="v">v. 114.</subfield><subfield code="0">http://id.loc.gov/authorities/names/n42015986</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=297165</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://www.sciencedirect.com/science/bookseries/00765392/114</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBL - Ebook Library</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL453170</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10329612</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">297165</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest MyiLibrary Digital eBook Collection</subfield><subfield code="b">IDEB</subfield><subfield code="n">229010</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn316568480 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:16:42Z |
| institution | BVB |
| isbn | 9780127289502 012728950X 9780080956237 0080956238 128229010X 9781282290105 |
| language | English |
| oclc_num | 316568480 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xiii, 331 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 1975 |
| publishDateSearch | 1975 |
| publishDateSort | 1975 |
| publisher | Academic Press, |
| record_format | marc |
| series | Mathematics in science and engineering ; |
| series2 | Mathematics in science and engineering ; |
| spelling | Wachspress, Eugene L. A rational finite element basis / Eugene L. Wachspress. New York : Academic Press, 1975. 1 online resource (xiii, 331 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Mathematics in science and engineering ; v. 114 Includes bibliographical references (pages 322-325) and index. Print version record. Use copy Restrictions unspecified star MiAaHDL A rational finite element basis. Electronic reproduction. [Place of publication not identified] : HathiTrust Digital Library, 2010. MiAaHDL Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL Front Cover; A Rational Finite Element Basis; Copyright Page; CONTENTS; PREFACE; THEOREMS AND LEMMAS; Chapter 1. PATCHWORK APPROXIMATION IN NUMERICAL ANALYSIS; 1.1 Wedges and Pyramids; 1.2 Definitions and Notation; 1.3 Continuity; 1.4 Patchwork Approximation Spaces and Convergence; 1.5 Wedge Properties; 1.6 Isoparametric Coordinates; 1.7 Generalizations to Sides of Higher Order and to Three-Dimensional Elements; 1.8 Remarks and References; Chapter 2. THE QUADRILATERAL; 2.1 Inadequacy of Polynomials; 2.2 Rational Wedges; 2.3 Areal Coordinates as Limits of Rational Wedges 2.4 An Example of Quadrilateral Wedges2.5 Projective Coordinates; 2.6 Polygons?; Chapter 3. RATIONAL WEDGES FOR SELECTED POLYCONS; 3.1 The 3-Con of Order Four; 3.2 The 4-Con of Order Five; 3.3 The Pentagon; 3.4 Some Elementary Congruences; 3.5 Wedges for 3-Cons of Orders Five and Six; 3.6 Two-sided Elements; 3.7 Related Studies; Chapter 4. ALGEBRAIC GEOMETRY FOUNDATIONS; 4.1 Motivation; 4.2 Homogeneous Coordinates and the Projective Plane; 4.3 Intersection of Plane Curves; 4.4 The Fundamental Congruence Theorem; 4.5 Associated Points; 4.6 Resolution of Singularities 4.7 Remarks and ReferencesChapter 5. RATIONAL WEDGE CONSTRUCTION FOR POLYCONS AND POLYPOLS; 5.1 Polycon Wedge Construction; 5.2 Verification of Polycon Wedge Properties; 5.3 The Case of the Vanishing Denominator; 5.4 Polypols and Deficit Intersection Points; 5.5 Polypol Wedge Numerators and Adjunct Intersection Points; 5.6 Illustrative Polycubes; Chapter 6. APPROXIMATION OF HIGHER DEGREE; 6.1 Data Fitting; 6.2 Degree Two Approximation; 6.3 Degree Three and Higher Degree Approximation; 6.4 Intermediate Approximation; 6.5 Higher Degree Approximation on Polypols 6.6 A Concise Algebraic Geometry Analysis6.7 Algebrais Reticulation; Chapter 7. THREE-DIMENSIONAL APPROXIMATION; 7.1 Definitions and Background; 7.2 Triangular Prisms and Hexahedra; 7.3 Polyhedra; 7.4 Polycondra; 7.5 The Adjoint of a Well-Set Polypoldron; 7.6 Polypoldra Nodes and Adjacent Factors for Degree k Approximation; 7.7 Attainment of Degree k Approximation; Chapter 8. A RATIONAL SOLUTION TO AN IRRATIONAL PROBLEM; 8.1 Irrational Wedges; 8.2 The Method of Descent; 8.3 Wedges for an Ill-Set Polycon; 8.4 Nonconvex Quadrilaterals; 8.5 Remarks; Chapter 9. FINITE ELEMENT DISCRETIZATION 9.1 Introductory Remarks9.2 Some Simple Quadrature Formulas; 9.3 Consistent Quadrature and the Patch Test; 9.4 Triangle Averaging; 9.5 Mosaic Discretization; 9.6 A Discrete Laplacian for Quadrilaterals; 9.7 Harmonious Discretization; Chapter 10. TWO-LEVEL COMPUTATION; 10.1 Recapitulation; 10.2 Synthesis; 10.3 Coarse Mesh Rebalancing; 10.4 Concluding Remarks; REFERENCES; INDEX Finite element method. http://id.loc.gov/authorities/subjects/sh85048349 Méthode des éléments finis. MATHEMATICS Differential Equations Partial. bisacsh Finite element method fast has work: A Rational finite element basis (Text) https://id.oclc.org/worldcat/entity/E39PCXCmFyk6tfQ4rGJY7cBWym https://id.oclc.org/worldcat/ontology/hasWork Print version: Wachspress, Eugene L. Rational finite element basis. New York : Academic Press, 1975 9780127289502 (DLC) 75012594 (OCoLC)1324549 Mathematics in science and engineering ; v. 114. http://id.loc.gov/authorities/names/n42015986 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=297165 Volltext FWS01 ZDB-4-EBA FWS_PDA_EBA https://www.sciencedirect.com/science/bookseries/00765392/114 Volltext |
| spellingShingle | Wachspress, Eugene L. A rational finite element basis / Mathematics in science and engineering ; Front Cover; A Rational Finite Element Basis; Copyright Page; CONTENTS; PREFACE; THEOREMS AND LEMMAS; Chapter 1. PATCHWORK APPROXIMATION IN NUMERICAL ANALYSIS; 1.1 Wedges and Pyramids; 1.2 Definitions and Notation; 1.3 Continuity; 1.4 Patchwork Approximation Spaces and Convergence; 1.5 Wedge Properties; 1.6 Isoparametric Coordinates; 1.7 Generalizations to Sides of Higher Order and to Three-Dimensional Elements; 1.8 Remarks and References; Chapter 2. THE QUADRILATERAL; 2.1 Inadequacy of Polynomials; 2.2 Rational Wedges; 2.3 Areal Coordinates as Limits of Rational Wedges 2.4 An Example of Quadrilateral Wedges2.5 Projective Coordinates; 2.6 Polygons?; Chapter 3. RATIONAL WEDGES FOR SELECTED POLYCONS; 3.1 The 3-Con of Order Four; 3.2 The 4-Con of Order Five; 3.3 The Pentagon; 3.4 Some Elementary Congruences; 3.5 Wedges for 3-Cons of Orders Five and Six; 3.6 Two-sided Elements; 3.7 Related Studies; Chapter 4. ALGEBRAIC GEOMETRY FOUNDATIONS; 4.1 Motivation; 4.2 Homogeneous Coordinates and the Projective Plane; 4.3 Intersection of Plane Curves; 4.4 The Fundamental Congruence Theorem; 4.5 Associated Points; 4.6 Resolution of Singularities 4.7 Remarks and ReferencesChapter 5. RATIONAL WEDGE CONSTRUCTION FOR POLYCONS AND POLYPOLS; 5.1 Polycon Wedge Construction; 5.2 Verification of Polycon Wedge Properties; 5.3 The Case of the Vanishing Denominator; 5.4 Polypols and Deficit Intersection Points; 5.5 Polypol Wedge Numerators and Adjunct Intersection Points; 5.6 Illustrative Polycubes; Chapter 6. APPROXIMATION OF HIGHER DEGREE; 6.1 Data Fitting; 6.2 Degree Two Approximation; 6.3 Degree Three and Higher Degree Approximation; 6.4 Intermediate Approximation; 6.5 Higher Degree Approximation on Polypols 6.6 A Concise Algebraic Geometry Analysis6.7 Algebrais Reticulation; Chapter 7. THREE-DIMENSIONAL APPROXIMATION; 7.1 Definitions and Background; 7.2 Triangular Prisms and Hexahedra; 7.3 Polyhedra; 7.4 Polycondra; 7.5 The Adjoint of a Well-Set Polypoldron; 7.6 Polypoldra Nodes and Adjacent Factors for Degree k Approximation; 7.7 Attainment of Degree k Approximation; Chapter 8. A RATIONAL SOLUTION TO AN IRRATIONAL PROBLEM; 8.1 Irrational Wedges; 8.2 The Method of Descent; 8.3 Wedges for an Ill-Set Polycon; 8.4 Nonconvex Quadrilaterals; 8.5 Remarks; Chapter 9. FINITE ELEMENT DISCRETIZATION 9.1 Introductory Remarks9.2 Some Simple Quadrature Formulas; 9.3 Consistent Quadrature and the Patch Test; 9.4 Triangle Averaging; 9.5 Mosaic Discretization; 9.6 A Discrete Laplacian for Quadrilaterals; 9.7 Harmonious Discretization; Chapter 10. TWO-LEVEL COMPUTATION; 10.1 Recapitulation; 10.2 Synthesis; 10.3 Coarse Mesh Rebalancing; 10.4 Concluding Remarks; REFERENCES; INDEX Finite element method. http://id.loc.gov/authorities/subjects/sh85048349 Méthode des éléments finis. MATHEMATICS Differential Equations Partial. bisacsh Finite element method fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85048349 |
| title | A rational finite element basis / |
| title_auth | A rational finite element basis / |
| title_exact_search | A rational finite element basis / |
| title_full | A rational finite element basis / Eugene L. Wachspress. |
| title_fullStr | A rational finite element basis / Eugene L. Wachspress. |
| title_full_unstemmed | A rational finite element basis / Eugene L. Wachspress. |
| title_short | A rational finite element basis / |
| title_sort | rational finite element basis |
| topic | Finite element method. http://id.loc.gov/authorities/subjects/sh85048349 Méthode des éléments finis. MATHEMATICS Differential Equations Partial. bisacsh Finite element method fast |
| topic_facet | Finite element method. Méthode des éléments finis. MATHEMATICS Differential Equations Partial. Finite element method |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=297165 https://www.sciencedirect.com/science/bookseries/00765392/114 |
| work_keys_str_mv | AT wachspresseugenel arationalfiniteelementbasis AT wachspresseugenel rationalfiniteelementbasis |