Finite element method books

Question

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!)

Answer 1

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.

Answer 2

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.

Answer 3

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.