# Numerical Approximation of Partial Differential Equations

• Matlab implementations illustrate the devised methods

• Problems, projects, and quizzes allow for self-evaluation

• Includes theoretical and physical backgrounds of mathematical models

Textbook

Part of the Texts in Applied Mathematics book series (TAM, volume 64)

1. Front Matter
Pages i-xv
2. ### Finite Differences and Finite Elements

1. Front Matter
Pages 1-1
2. Sören Bartels
Pages 3-64
3. Sören Bartels
Pages 65-97
4. Sören Bartels
Pages 99-152
3. ### Local Resolution and Iterative Solution

1. Front Matter
Pages 153-153
2. Sören Bartels
Pages 155-207
3. Sören Bartels
Pages 209-244
4. ### Constrained and Singularly Perturbed Problems

1. Front Matter
Pages 245-245
2. Sören Bartels
Pages 247-281
3. Sören Bartels
Pages 283-347
4. Sören Bartels
Pages 349-404
5. Back Matter
Pages 405-535

### Introduction

Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular applications including incompressible elasticity, thin elastic objects, electromagnetism, and fluid mechanics are addressed. The book includes theoretical problems and practical projects for all chapters, and an introduction to the implementation of finite element methods.

### Keywords

finite element methods numerical analysis partial differential equations iterative solution methods convergence analysis

#### Authors and affiliations

1. 1.Angewandte MathematikAlbert-Ludwigs-UniversitaetFreiburgGermany

Sören Bartels is Professor of Applied Mathematics at the Albert-Ludwigs University in Freiburg, Germany. His primary research interest is in the development and analysis of approximation schemes for nonlinear partial differential equations with applications in the simulation of modern materials. Professor Bartels has published the Springer textbook "Numerik 3x9" and the monograph "Numerical methods for nonlinear partial differential equations" in the Springer Series in Computational Mathematics.

### Bibliographic information

• Book Title Numerical Approximation of Partial Differential Equations
• Authors Sören Bartels
• Series Title Texts in Applied Mathematics
• Series Abbreviated Title Texts in Applied Math.
• DOI https://doi.org/10.1007/978-3-319-32354-1
• Copyright Information Springer International Publishing Switzerland 2016
• Publisher Name Springer, Cham
• eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
• Hardcover ISBN 978-3-319-32353-4
• Softcover ISBN 978-3-319-81265-6
• eBook ISBN 978-3-319-32354-1
• Series ISSN 0939-2475
• Series E-ISSN 2196-9949
• Edition Number 1
• Number of Pages XV, 535
• Number of Illustrations 170 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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