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I know this question has been asked before; I just want to enquire if anybody has any suggestions to learn how to compute finite element problems, including plenty of examples.

The topics I would like to focus in are as follows:

Introduction to finite elements for 1D and 2D problems covering:

  • weak formulation
  • Galerkin approximation
  • Shape functions
  • Isoparametric elements

Key examples with walkthrough of common problems such as:

  • Applying to heat equation
  • Applying to beam equation
  • Eigenvalue Problems
  • Nonlinear Problems

Any recommendations would be sincerely appreciated (and happy new year!)

MKF
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3 Answers3

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I would suggest Larson–Bengzon - The Finite Element Method: Theory, Implementation and Applications. It contains everything you requested for. They use Matlab as a programming environment.

knl
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A good introductory book is "Understanding and implementing the finite element method" from Mark S. Gockenbach. Some of your listed examples are covered by implementations of the method.

tstudio
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I suggest the book Numerical Solution of Partial Differential Equations by the Finite Element Method by Claes Johnson. I think, it chooses the right level of abstraction for a first book on this topic.

H. Rittich
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