Introduction to Sobolev spaces and finite element solution of elliptic boundary value problems:
Gespeichert in:
| 1. Verfasser: | |
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| Weitere Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London ; Orlando ; San Diego ; New York ; Austin ; Boston ; Sydney ; Tokyo ; Toronto
Academic Press
1986
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| Schriftenreihe: | Computational mathematics and applications
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus d. Dt. übers. |
| Beschreibung: | viii, 211 Seiten Diagramme |
| ISBN: | 0124745105 |
Internformat
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| 245 | 1 | 0 | |a Introduction to Sobolev spaces and finite element solution of elliptic boundary value problems |c J. T. Marti ; J. R. Whiteman |
| 264 | 1 | |a London ; Orlando ; San Diego ; New York ; Austin ; Boston ; Sydney ; Tokyo ; Toronto |b Academic Press |c 1986 | |
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| 650 | 4 | |a Équations différentielles elliptiques - Solutions numériques | |
| 650 | 4 | |a Boundary value problems |x Numerical solutions | |
| 650 | 4 | |a Differential equations, Elliptic |x Numerical solutions | |
| 650 | 4 | |a Finite element method | |
| 650 | 4 | |a Sobolev spaces | |
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Datensatz im Suchindex
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Titel: Introduction to Sobolev spaces and finite element solution of elliptic boundary value problems
Autor: Marti, Jürg T
Jahr: 1986
Contents Preface. v List of symbols. ix 1 Convolutions and Mollifiers. 1 1.1 Approximation by continuous functions in L 2 (G) . 1 1.2 Properties of convolutions. 6 1.3 Mollifiers. 13 1.4 Approximation by smooth functions in L 2 (G). 15 1.5 Weyl’s Lemma on harmonic functions. 16 2 Sobolev Spaces on One-Dimensional Intervals. 21 2.1 Sobolev spaces as completions of dense sets. 22 2.2 Imbedding and trace theorems. 25 2.3 An extension theorem and inequalities. 35 2.4 Sobolev spaces of periodic functions. 42 3 Sobolev Spaces H m (G) on Domains G in R". 49 3.1 H m (G) as completion of C m (G). 49 3.2 The Sobolev space H m (U n ) . 53 3.3 Traces of functions defined on a half-space. 58 3.4 Sobolev spaces H m (G) for Lipschitz domains G. 59 4 The Inequalities of Poincare and Friedrichs. 67 4.1 The compact imbedding of H m (G) into H m ~ 1 (G) . 67 4.2 Poincare’s inequality. 72 4.3 The trace operator for Lipschitz domains G. 77 4.4 Friedrichs’ inequality. 82 5 Extension Theorems. 85 5.1 The Calderon-Zygmund inequality. 85 5.2 An extension operator. 90 5.3 Calderon’s extension theorem. 94
Contents vin 6 Imbeddings of H m (G) . 97 6.1 The imbeding of H m (G) into C(G). 97 6.2 Compactness of the imbedding of H m (G) into C(G ). 105 7 Elliptic Boundary Value Problems.111 7.1 Boundary value problems with elliptic differential operators.Ill 7.2 V-elliptic bilinear forms.115 7.3 Weak forms of elliptic boundary value problems . 119 7.4 Examples of elliptic boundary value problems of order 2 and 4.122 7.5 Weak and classical solutions of the Poisson problem . . . 134 7.6 Examples concerning the regularity of the solution of a Poisson problem.145 7.7 Regularity for the Poisson problem for convex polygonal domains.154 8 The Finite Element Method for the Solution of Elliptic Boundary Value Problems.165 8.1 Piecewise-polynomial functions in C k ~\G) .165 8.2 Approximation in H k {G) by piecewise-polynomial functions.177 8.3 Numerical solution of elliptic boundary value problems by the finite element method.181 8.4 Computation of the matrix elements.184 8.5 Explicit numerical solution of a two-dimensional Poisson problem.191 8.6 An example for the approximate solution of a variational problem.195 8.7 Convergence properties of the finite element method . . 199 References.205 Subject Index.208 |
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| author | Marti, Jürg Thomas 1935- |
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| isbn | 0124745105 |
| language | English |
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| physical | viii, 211 Seiten Diagramme |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Academic Press |
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| series2 | Computational mathematics and applications |
| spelling | Marti, Jürg Thomas 1935- (DE-588)125403003 aut Introduction to Sobolev spaces and finite element solution of elliptic boundary value problems J. T. Marti ; J. R. Whiteman London ; Orlando ; San Diego ; New York ; Austin ; Boston ; Sydney ; Tokyo ; Toronto Academic Press 1986 viii, 211 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Computational mathematics and applications Aus d. Dt. übers. Problèmes aux limites - Solutions numériques Sobolev, Espaces de Éléments finis, Méthode des Équations aux dérivées partielles - Solutions numériques Équations différentielles elliptiques - Solutions numériques Boundary value problems Numerical solutions Differential equations, Elliptic Numerical solutions Finite element method Sobolev spaces Randwertproblem (DE-588)4048395-2 gnd rswk-swf Elliptisches Randwertproblem (DE-588)4193399-0 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Sobolev-Raum (DE-588)4055345-0 gnd rswk-swf Sobolev-Raum (DE-588)4055345-0 s DE-604 Elliptisches Randwertproblem (DE-588)4193399-0 s Finite-Elemente-Methode (DE-588)4017233-8 s Randwertproblem (DE-588)4048395-2 s Elliptische Differentialgleichung (DE-588)4014485-9 s Whiteman, John R. 1938- (DE-588)124182364 edt HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003868343&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Marti, Jürg Thomas 1935- Introduction to Sobolev spaces and finite element solution of elliptic boundary value problems Problèmes aux limites - Solutions numériques Sobolev, Espaces de Éléments finis, Méthode des Équations aux dérivées partielles - Solutions numériques Équations différentielles elliptiques - Solutions numériques Boundary value problems Numerical solutions Differential equations, Elliptic Numerical solutions Finite element method Sobolev spaces Randwertproblem (DE-588)4048395-2 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Sobolev-Raum (DE-588)4055345-0 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4193399-0 (DE-588)4014485-9 (DE-588)4017233-8 (DE-588)4055345-0 |
| title | Introduction to Sobolev spaces and finite element solution of elliptic boundary value problems |
| title_auth | Introduction to Sobolev spaces and finite element solution of elliptic boundary value problems |
| title_exact_search | Introduction to Sobolev spaces and finite element solution of elliptic boundary value problems |
| title_full | Introduction to Sobolev spaces and finite element solution of elliptic boundary value problems J. T. Marti ; J. R. Whiteman |
| title_fullStr | Introduction to Sobolev spaces and finite element solution of elliptic boundary value problems J. T. Marti ; J. R. Whiteman |
| title_full_unstemmed | Introduction to Sobolev spaces and finite element solution of elliptic boundary value problems J. T. Marti ; J. R. Whiteman |
| title_short | Introduction to Sobolev spaces and finite element solution of elliptic boundary value problems |
| title_sort | introduction to sobolev spaces and finite element solution of elliptic boundary value problems |
| topic | Problèmes aux limites - Solutions numériques Sobolev, Espaces de Éléments finis, Méthode des Équations aux dérivées partielles - Solutions numériques Équations différentielles elliptiques - Solutions numériques Boundary value problems Numerical solutions Differential equations, Elliptic Numerical solutions Finite element method Sobolev spaces Randwertproblem (DE-588)4048395-2 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Sobolev-Raum (DE-588)4055345-0 gnd |
| topic_facet | Problèmes aux limites - Solutions numériques Sobolev, Espaces de Éléments finis, Méthode des Équations aux dérivées partielles - Solutions numériques Équations différentielles elliptiques - Solutions numériques Boundary value problems Numerical solutions Differential equations, Elliptic Numerical solutions Finite element method Sobolev spaces Randwertproblem Elliptisches Randwertproblem Elliptische Differentialgleichung Finite-Elemente-Methode Sobolev-Raum |
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