The Finite Element Method: Theory, Implementation, and Applications

  • Mats G. Larson
  • Fredrik Bengzon

Part of the Texts in Computational Science and Engineering book series (TCSE, volume 10)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Mats G. Larson, Fredrik Bengzon
    Pages 1-22
  3. Mats G. Larson, Fredrik Bengzon
    Pages 23-44
  4. Mats G. Larson, Fredrik Bengzon
    Pages 45-69
  5. Mats G. Larson, Fredrik Bengzon
    Pages 71-111
  6. Mats G. Larson, Fredrik Bengzon
    Pages 113-142
  7. Mats G. Larson, Fredrik Bengzon
    Pages 143-176
  8. Mats G. Larson, Fredrik Bengzon
    Pages 177-201
  9. Mats G. Larson, Fredrik Bengzon
    Pages 203-223
  10. Mats G. Larson, Fredrik Bengzon
    Pages 225-239
  11. Mats G. Larson, Fredrik Bengzon
    Pages 241-256
  12. Mats G. Larson, Fredrik Bengzon
    Pages 257-287
  13. Mats G. Larson, Fredrik Bengzon
    Pages 289-325
  14. Mats G. Larson, Fredrik Bengzon
    Pages 327-354
  15. Mats G. Larson, Fredrik Bengzon
    Pages 355-372
  16. Back Matter
    Pages 373-385

About this book

Introduction

This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.​    

Keywords

adaptive finite element methods applications of finite elements error estimates finite element method implementation of finite elements

Authors and affiliations

  • Mats G. Larson
    • 1
  • Fredrik Bengzon
    • 2
  1. 1., Department of MathematicsUmeå UniversityUmeaSweden
  2. 2., Department of MathematicsUmeå UniversityUmeaSweden

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-33287-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-33286-9
  • Online ISBN 978-3-642-33287-6
  • Series Print ISSN 1611-0994
  • About this book
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