MTH 654/ 659 (Numerical Analysis) Fall 2011
Finite Element Methods for Partial Differential Equations
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General information
Textbook and resources
Assignments
Textbook and resources:
  • Official textbook for class is Finite Elements : Theory, Fast Solvers, and Applications in Solid Mechanics by Dietrich Braess, Cambridge University Press; 3rd edition, 2007 ISBN-13: 9780521705189
    Please note that this information applies to the Paperback (III Edition). A used version of the Hardcover version or Second Edition *may* also work.
  • I will not follow the book religiously but rather use it for background information. We will cover roughly material from Chapters II, some from I and III, IV. Some topics will be discussed but are not covered in the book.
  • Other textbooks/monographs (each of a very different flavor) are recommended as supplementary material
    • "Numerical solution of partial differential equations by the finite element method", Claes Johnson, Dover, 2009 (originally by Cambridge University Press, 1987)
    • "The mathematical theory of finite element methods", Susanne C. Brenner, L. Ridgway Scott, New York : Springer, 2002.
    • "Finite Elements and Fast Iterative Solvers with applications to incompressible fluid dynamics", H. Elman, D. Silvester, A. Wathen, Oxford Science Publishers, 2005
    • The classic by Becker, Carey, Oden: "Finite Elements" Vol I-VI. Prentice-Hall, 1983 (out of print)
    • An Introduction to the Mathematical Theory of Finite Elements by Oden, Reddy, Dover, 2011 (originally Wiley, 1976)
    • Another classic approach, this one for parabolic problems: "Galerkin Finite Element Methods for Parabolic Problems", Vidar Thomee, Springer 2006
    • Ciarlet's book reprinted by SIAM: P. G. Ciarlet: "The Finite Element Method for Elliptic Problems", SIAM, 2002 (Originally published by North Holland, 1980).
    • "Finite Element Methods and Their Applications" (Scientific Computation) (Hardcover) by Zhangxin Chen (Springer, 2005)
    • "Numerical approximation of partial differential equations", by Alfio Quarteroni, Alberto Valli, Springer-Verlag, 1994
    • The first texbook on FE: "An analysis of the finite element method", Gilbert Strang and George J. Fix. Prentice-Hall, 1973
    • Class notes on Variational Method in Hilbert Space by Ralph E. Showalter
  • Software: