Numerical Approximation of Partial Differential Equations

  • Sören Bartels

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

Table of contents

  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

About this book

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

  • Sören Bartels
    • 1
  1. 1.Angewandte MathematikAlbert-Ludwigs-UniversitaetFreiburgGermany

Bibliographic information

  • 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
  • Print ISBN 978-3-319-32353-4
  • Online ISBN 978-3-319-32354-1
  • Series Print ISSN 0939-2475
  • Series Online ISSN 2196-9949
  • About this book