Finite element methods with B-splines:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia
Soc. for Industrial and Applied Mathematics
2003
|
| Schriftenreihe: | Frontiers in applied mathematics
|
| Schlagworte: | |
| Online-Zugang: | Table of contents Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 137-142) and index |
| Beschreibung: | X, 145 S. graph. Darst. |
| ISBN: | 0898715334 |
Internformat
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV014794720 | ||
| 003 | DE-604 | ||
| 005 | 20060425 | ||
| 007 | t | ||
| 008 | 021008s2003 xxud||| |||| 00||| eng d | ||
| 010 | |a 2002036509 | ||
| 020 | |a 0898715334 |9 0-89871-533-4 | ||
| 035 | |a (OCoLC)50725097 | ||
| 035 | |a (DE-599)BVBBV014794720 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-703 |a DE-91G |a DE-20 |a DE-91 |a DE-824 |a DE-634 |a DE-83 | ||
| 050 | 0 | |a TA645 | |
| 082 | 0 | |a 620/.001/51535 |2 21 | |
| 084 | |a SK 910 |0 (DE-625)143270: |2 rvk | ||
| 084 | |a 74S05 |2 msc | ||
| 084 | |a MAT 674f |2 stub | ||
| 084 | |a 65N30 |2 msc | ||
| 084 | |a 65D07 |2 msc | ||
| 100 | 1 | |a Höllig, Klaus |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Finite element methods with B-splines |c Klaus Höllig |
| 264 | 1 | |a Philadelphia |b Soc. for Industrial and Applied Mathematics |c 2003 | |
| 300 | |a X, 145 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Frontiers in applied mathematics | |
| 500 | |a Includes bibliographical references (p. 137-142) and index | ||
| 650 | 4 | |a Constructions, Théorie des | |
| 650 | 4 | |a Splines, Théorie des | |
| 650 | 4 | |a Éléments finis, Méthode des | |
| 650 | 4 | |a Finite element method | |
| 650 | 4 | |a Spline theory | |
| 650 | 4 | |a Structural analysis (Engineering) | |
| 650 | 0 | 7 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a B-Spline |0 (DE-588)4384798-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Finite-Elemente-Methode |0 (DE-588)4017233-8 |D s |
| 689 | 0 | 1 | |a B-Spline |0 (DE-588)4384798-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | |u http://www.loc.gov/catdir/toc/fy037/2002036509.html |3 Table of contents | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010011886&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-010011886 | ||
Datensatz im Suchindex
| _version_ | 1804129570274672640 |
|---|---|
| adam_text | Contents
Preface ix
1 Introduction 1
2 Basic Finite Element Concepts 7
2.1 Model Problem 7
2.2 Mesh Based Elements 9
2.3 Sobolev Spaces 12
2.4 Abstract Variational Problems 16
2.5 Approximation Error 19
3 B Splines 23
3.1 The Concept of Splines 23
3.2 Definition and Basic Properties 25
3.3 Recurrence Relation 27
3.4 Representation of Polynomials 29
3.5 Subdivision 32
3.6 Scalar Products 35
4 Finite Element Bases 37
4.1 Multivariate B Splines 37
4.2 Splines on Bounded Domains 40
4.3 Weight Functions 43
4.4 Web Splines 46
4.5 Hierarchical Bases 50
5 Approximation with Weighted Splines 53
5.1 Dual Functions 53
5.2 Stability 56
5.3 Polynomial Approximation 60
5.4 Quasi Interpolation 63
5.5 Boundary Regularity 65
5.6 Error Estimates for Standard Weight Functions 67
vii
viii Contents
6 Boundary Value Problems 71
6.1 Essential Boundary Conditions 71
6.2 Natural Boundary Conditions 75
6.3 Mixed Problems with Variable Coefficients 79
6.4 Biharmonic Equation 82
6.5 Linear Elasticity 86
6.6 Plane Strain and Plane Stress 89
7 Multigrid Methods 95
7.1 Multigrid Idea 95
7.2 Grid Transfer 99
7.3 Basic Algorithm 103
7.4 Smoothing and Coarse Grid Approximation 105
7.5 Convergence 108
8 Implementation 113
8.1 Boundary Representation 114
8.2 Classification of Grid Cells 116
8.3 Evaluation of Weight Functions 119
8.4 Numerical Integration 124
8.5 Matrix Assembly 127
Appendix 131
Notation and Symbols 135
Bibliography 137
Index 143
|
| any_adam_object | 1 |
| author | Höllig, Klaus |
| author_facet | Höllig, Klaus |
| author_role | aut |
| author_sort | Höllig, Klaus |
| author_variant | k h kh |
| building | Verbundindex |
| bvnumber | BV014794720 |
| callnumber-first | T - Technology |
| callnumber-label | TA645 |
| callnumber-raw | TA645 |
| callnumber-search | TA645 |
| callnumber-sort | TA 3645 |
| callnumber-subject | TA - General and Civil Engineering |
| classification_rvk | SK 910 |
| classification_tum | MAT 674f |
| ctrlnum | (OCoLC)50725097 (DE-599)BVBBV014794720 |
| dewey-full | 620/.001/51535 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620/.001/51535 |
| dewey-search | 620/.001/51535 |
| dewey-sort | 3620 11 551535 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02014nam a2200541zc 4500</leader><controlfield tag="001">BV014794720</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20060425 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">021008s2003 xxud||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2002036509</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0898715334</subfield><subfield code="9">0-89871-533-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)50725097</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV014794720</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">TA645</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">620/.001/51535</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 910</subfield><subfield code="0">(DE-625)143270:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">74S05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 674f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">65N30</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">65D07</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Höllig, Klaus</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Finite element methods with B-splines</subfield><subfield code="c">Klaus Höllig</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Philadelphia</subfield><subfield code="b">Soc. for Industrial and Applied Mathematics</subfield><subfield code="c">2003</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 145 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Frontiers in applied mathematics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (p. 137-142) and index</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Constructions, Théorie des</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Splines, Théorie des</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Éléments finis, Méthode des</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Finite element method</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Spline theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Structural analysis (Engineering)</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Finite-Elemente-Methode</subfield><subfield code="0">(DE-588)4017233-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">B-Spline</subfield><subfield code="0">(DE-588)4384798-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Finite-Elemente-Methode</subfield><subfield code="0">(DE-588)4017233-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">B-Spline</subfield><subfield code="0">(DE-588)4384798-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">http://www.loc.gov/catdir/toc/fy037/2002036509.html</subfield><subfield code="3">Table of contents</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010011886&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-010011886</subfield></datafield></record></collection> |
| id | DE-604.BV014794720 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:07:14Z |
| institution | BVB |
| isbn | 0898715334 |
| language | English |
| lccn | 2002036509 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010011886 |
| oclc_num | 50725097 |
| open_access_boolean | |
| owner | DE-703 DE-91G DE-BY-TUM DE-20 DE-91 DE-BY-TUM DE-824 DE-634 DE-83 |
| owner_facet | DE-703 DE-91G DE-BY-TUM DE-20 DE-91 DE-BY-TUM DE-824 DE-634 DE-83 |
| physical | X, 145 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Soc. for Industrial and Applied Mathematics |
| record_format | marc |
| series2 | Frontiers in applied mathematics |
| spelling | Höllig, Klaus Verfasser aut Finite element methods with B-splines Klaus Höllig Philadelphia Soc. for Industrial and Applied Mathematics 2003 X, 145 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Frontiers in applied mathematics Includes bibliographical references (p. 137-142) and index Constructions, Théorie des Splines, Théorie des Éléments finis, Méthode des Finite element method Spline theory Structural analysis (Engineering) Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf B-Spline (DE-588)4384798-5 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 s B-Spline (DE-588)4384798-5 s DE-604 http://www.loc.gov/catdir/toc/fy037/2002036509.html Table of contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010011886&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Höllig, Klaus Finite element methods with B-splines Constructions, Théorie des Splines, Théorie des Éléments finis, Méthode des Finite element method Spline theory Structural analysis (Engineering) Finite-Elemente-Methode (DE-588)4017233-8 gnd B-Spline (DE-588)4384798-5 gnd |
| subject_GND | (DE-588)4017233-8 (DE-588)4384798-5 |
| title | Finite element methods with B-splines |
| title_auth | Finite element methods with B-splines |
| title_exact_search | Finite element methods with B-splines |
| title_full | Finite element methods with B-splines Klaus Höllig |
| title_fullStr | Finite element methods with B-splines Klaus Höllig |
| title_full_unstemmed | Finite element methods with B-splines Klaus Höllig |
| title_short | Finite element methods with B-splines |
| title_sort | finite element methods with b splines |
| topic | Constructions, Théorie des Splines, Théorie des Éléments finis, Méthode des Finite element method Spline theory Structural analysis (Engineering) Finite-Elemente-Methode (DE-588)4017233-8 gnd B-Spline (DE-588)4384798-5 gnd |
| topic_facet | Constructions, Théorie des Splines, Théorie des Éléments finis, Méthode des Finite element method Spline theory Structural analysis (Engineering) Finite-Elemente-Methode B-Spline |
| url | http://www.loc.gov/catdir/toc/fy037/2002036509.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010011886&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT holligklaus finiteelementmethodswithbsplines |