The Mathematical Theory of Finite Element Methods

The Mathematical Theory of Finite Element Methods

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This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. One purpose of this book is to formalize basic tools that are commonly used by researchers in the field but never published. The results contained here have never appeared before, and should prove interesting to researchers. It is intended primarily for Ist year mathematics graduate students and mathematically sophisticated engineers and scientists.
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Product details

  • Hardback | 306 pages
  • 138 x 216mm | 585g
  • Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Berlin, Germany
  • 38 figures
  • 3540941932
  • 9783540941934

Table of contents

Contents: Basic Concepts.- Sobolev Spaces.- Variational Formulation of Elliptic Boundary Value Problems.- The Construction of a Finite Element Space.- Polynomial Approximation Theory in Sobolev Spaces.- n-Dimensional Variational Problems.- Variational Approximation of Poisson's Equation.- Finite Element Multigrid Methods.- Max-norm Estimates.- Variational Crimes.- Applications to Planar Elasticity.- Mixed Methods.- Iterative Techniques for Mixed Methods.- Applications of Operator-Interpolation Theory.
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