We will use two classic (and inexpensive) textbooks, each oriented at a different audience
-
"Numerical solution of partial differential equations by the
finite element method", Claes Johnson, Dover, 2009 (originally by Cambridge
University Press, 1987)
-
"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 books very closely but rather use it for
background information.
From (1, Johnson), we will cover Chapters 1-4, selected topics from 5-7, and 8-12.
From (2, Braess), 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 books.
Other textbooks/monographs (each of a very different flavor) are
recommended as supplementary material
-
"The mathematical theory of finite element methods", Susanne
C. Brenner, L. Ridgway Scott, New York : Springer, 2002.
- "Finite Element Methods and Their Applications" (Scientific Computation) (Hardcover)
by Zhangxin Chen (Springer, 2005)
-
"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
-
Discontinuous Galerkin Methods For Solving Elliptic and Parabolic Equations: Theory and Implementation (SIAM Frontiers in Applied Mathematics), by
Beatrice M. Riviere, 2008
-
Adaptive Finite Element Methods for Differential Equations (Lectures
in Mathematics. Wolfgang Bangerth and Rolf Rannacher,
ETH Zurich, 2003
- Ciarlet's classic reprinted by SIAM:
P. G. Ciarlet:
"The Finite Element Method for Elliptic Problems",
SIAM, 2002 (Originally published by North Holland, 1980).
- "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:
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