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Some books on the finite element method
Literature on learning finite elements
Dietrich Braess: Finite Elements : Theory, Fast Solvers, and Applications in Solid Mechanics, Cambridge
- Exposition of the method and theoretical results with some not so standard applications
Susanne C. Brenner, L. Ridgway Scott: The Mathematical Theory of Finite Element Methods, Springer, 2002
- Excellent introduction into the theory of finite elements, including multigrid and Schwarz solvers. Recommended for mathematicians.
Philippe G. Ciarlet: The Finite Element Method for Elliptic Problems, SIAM Classics in Applied Mathematics
- Very abstract, but still the bible.
Christian Großmann, Hans-Görg Roos: Numerik partieller Differentialgleichungen, Teubner
- Probably the best exposition for students and researchers available.
Hans Rudolf Schwarz: Methode der finiten Elemente, Teubner
- Although some of the coding considerations are hopelessly outdated, the book is a good introduction to finite elements from a practical point of view.