Numerical methods for elliptic and parabolic partial differential equations:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
New York [u.a.]
Springer
2003
|
| Series: | Texts in applied mathematics
44 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XV, 424 S. graph. Darst. |
| ISBN: | 038795449X |
Staff View
MARC
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| 100 | 1 | |a Knabner, Peter |d 1954- |e Verfasser |0 (DE-588)110505824 |4 aut | |
| 240 | 1 | 0 | |a Numerik partieller Differentialgleichungen |
| 245 | 1 | 0 | |a Numerical methods for elliptic and parabolic partial differential equations |c Peter Knabner ; Lutz Angermann |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2003 | |
| 300 | |a XV, 424 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Texts in applied mathematics |v 44 | |
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| 650 | 4 | |a Équations aux dérivées partielles - Solutions numériques | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Series Preface v
Preface to the English Edition vii
Preface to the German Edition xi
0 For Example: Modelling Processes in Porous Media
with Differential Equations 1
0.1 The Basic Partial Differential Equation Models 1
0.2 Reactions and Transport in Porous Media 5
0.3 Fluid Flow in Porous Media 7
0.4 Reactive Solute Transport in Porous Media 11
0.5 Boundary and Initial Value Problems 14
1 For the Beginning: The Finite Difference Method
for the Poisson Equation 19
1.1 The Dirichlet Problem for the Poisson Equation 19
1.2 The Finite Difference Method 21
1.3 Generalizations and Limitations
of the Finite Difference Method 29
1.4 Maximum Principles and Stability 36
2 The Finite Element Method for the Poisson Equation 46
2.1 Variational Formulation for the Model Problem 46
xiv Contents
2.2 The Finite Element Method with Linear Elements .... 55
2.3 Stability and Convergence of the
Finite Element Method 68
2.4 The Implementation of the Finite Element Method:
Part 1 74
2.5 Solving Sparse Systems of Linear Equations
by Direct Methods 82
3 The Finite Element Method for Linear Elliptic
Boundary Value Problems of Second Order 92
3.1 Variational Equations and Sobolev Spaces 92
3.2 Elliptic Boundary Value Problems of Second Order . . . 100
3.3 Element Types and Affine
Equivalent Triangulations 114
3.4 Convergence Rate Estimates 131
3.5 The Implementation of the Finite Element Method:
Part 2 148
3.6 Convergence Rate Results in Case of
Quadrature and Interpolation 155
3.7 The Condition Number of Finite Element Matrices . . . 163
3.8 General Domains and Isoparametric Elements 167
3.9 The Maximum Principle for Finite Element Methods . . 171
4 Grid Generation and A Posteriori Error Estimation 176
4.1 Grid Generation 176
4.2 A Posteriori Error Estimates and Grid Adaptation . . . 185
5 Iterative Methods for Systems of Linear Equations 198
5.1 Linear Stationary Iterative Methods 200
5.2 Gradient and Conjugate Gradient Methods 217
5.3 Preconditioned Conjugate Gradient Method 227
5.4 Krylov Subspace Methods
for Nonsymmetric Systems of Equations 233
5.5 The Multigrid Method 238
5.6 Nested Iterations 251
6 The Finite Volume Method 255
6.1 The Basic Idea of the Finite Volume Method 256
6.2 The Finite Volume Method for Linear Elliptic Differen¬
tial Equations of Second Order on Triangular Grids . . . 262
7 Discretization Methods for Parabolic Initial Boundary
Value Problems 283
7.1 Problem Setting and Solution Concept 283
7.2 Semidiscretization by the Vertical Method of Lines . . . 293
Contents xv
7.3 Fully Discrete Schemes 311
7.4 Stability 315
7.5 The Maximum Principle for the
One Step Theta Method 323
7.6 Order of Convergence Estimates 330
8 Iterative Methods for Nonlinear Equations 342
8.1 Fixed Point Iterations 344
8.2 Newton s Method and Its Variants 348
8.3 Semilinear Boundary Value Problems for Elliptic
and Parabolic Equations 360
9 Discretization Methods
for Convection Dominated Problems 368
9.1 Standard Methods and
Convection Dominated Problems 368
9.2 The Streamline Diffusion Method 375
9.3 Finite Volume Methods 383
9.4 The Lagrange Galerkin Method 387
A Appendices 390
A.I Notation 390
A.2 Basic Concepts of Analysis 393
A.3 Basic Concepts of Linear Algebra 394
A.4 Some Definitions and Arguments of Linear
Functional Analysis 399
A.5 Function Spaces 404
References: Textbooks and Monographs 409
References: Journal Papers 412
Index 415
|
| any_adam_object | 1 |
| author | Knabner, Peter 1954- Angermann, Lutz |
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| author_facet | Knabner, Peter 1954- Angermann, Lutz |
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| author_sort | Knabner, Peter 1954- |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV015470801 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:09:21Z |
| institution | BVB |
| isbn | 038795449X |
| language | English German |
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| physical | XV, 424 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
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| publisher | Springer |
| record_format | marc |
| series | Texts in applied mathematics |
| series2 | Texts in applied mathematics |
| spelling | Knabner, Peter 1954- Verfasser (DE-588)110505824 aut Numerik partieller Differentialgleichungen Numerical methods for elliptic and parabolic partial differential equations Peter Knabner ; Lutz Angermann New York [u.a.] Springer 2003 XV, 424 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 44 Includes bibliographical references and index Equações diferenciais parciais larpcal Équations aux dérivées partielles - Solutions numériques Differential equations, Partial -- Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Partielle Differentialgleichung (DE-588)4044779-0 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Numerische Mathematik (DE-588)4042805-9 s 1\p DE-604 Angermann, Lutz Verfasser (DE-588)101487727X aut Texts in applied mathematics 44 (DE-604)BV002476038 44 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010110107&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Knabner, Peter 1954- Angermann, Lutz Numerical methods for elliptic and parabolic partial differential equations Texts in applied mathematics Equações diferenciais parciais larpcal Équations aux dérivées partielles - Solutions numériques Differential equations, Partial -- Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4042805-9 (DE-588)4044779-0 (DE-588)4123623-3 |
| title | Numerical methods for elliptic and parabolic partial differential equations |
| title_alt | Numerik partieller Differentialgleichungen |
| title_auth | Numerical methods for elliptic and parabolic partial differential equations |
| title_exact_search | Numerical methods for elliptic and parabolic partial differential equations |
| title_full | Numerical methods for elliptic and parabolic partial differential equations Peter Knabner ; Lutz Angermann |
| title_fullStr | Numerical methods for elliptic and parabolic partial differential equations Peter Knabner ; Lutz Angermann |
| title_full_unstemmed | Numerical methods for elliptic and parabolic partial differential equations Peter Knabner ; Lutz Angermann |
| title_short | Numerical methods for elliptic and parabolic partial differential equations |
| title_sort | numerical methods for elliptic and parabolic partial differential equations |
| topic | Equações diferenciais parciais larpcal Équations aux dérivées partielles - Solutions numériques Differential equations, Partial -- Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Equações diferenciais parciais Équations aux dérivées partielles - Solutions numériques Differential equations, Partial -- Numerical solutions Numerisches Verfahren Numerische Mathematik Partielle Differentialgleichung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010110107&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002476038 |
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