There are many books and websites that present material relevant to
this course. The following are a few suggestions, but these are
neither required reading nor a complete list of good references.
Finite Difference Schemes and Partial Differential Equations, by
John C. Strikwerda, SIAM 2004
Finite Difference Methods for Ordinary and Partial Differential
Equations, by Randall J. Leveque, SIAM 2007
Principles of Computational Fluid Dynamics, by Pieter Wesseling,
Springer 2001
A First Course in the Numerical Analysis of Differential
Equations, by Arieh Iserles, Cambridge University Press 1996
Introduction
to Computational PDEs, by Hans De Sterck and Paul Ullrich,
University of Waterloo 2009
The Mathematical Theory of Finite Element Methods, by Suzanne
Brenner and Ridgeway Scott, Springer 1994
Finite Elements: Theory, fast solvers, and applications in solid
mechanics, by Dietrich Braess, Cambridge University Press 2001
Finite Elements and Fast Iterative Solvers with applications in
incompressible fluid dynamics, by Howard Elman, David Silvester, and
Andy Wathen, Oxford Science Publications 2005
Matrix Iterative Analysis, by Richard Varga, Springer 2000
Iterative Methods for Sparse Linear Systems, by Yousef Saad, SIAM
2003. First edition
available here
Iterative Methods for Solving Linear Systems, by Anne Greenbaum,
SIAM 1997
A Multigrid Tutorial, by William Briggs, Van Emden Henson, and
Steve McCormick, SIAM 2000. Accompanying slides available here
Multigrid, by Ulrich Trottenberg, Cornelis Oosterlee, and Anton
Schüller, Elsevier 2001
