References for Math 425, Fall 2002


On reserve in the mathematics library:

Ivo Babuska and Theofanis Strouboulis, The Finite Element method and its Reliability, Oxford University Press, Oxford, UK, 2001. Gives a fairly comprehensive theoretical reference for the differential equations/finite element portions of Math 425. It illustrates concepts in the finite element method by first discussing them in the simpler setting of the two-point boundary value problem, then moving on to the more complicated higher-dimensional PDE setting.


On reserve in the engineering library:

Charles F. Van Loan, Introduction to Scientific Computing: A Matrix-Vector Approach using MATLAB, 2nd ed., Prentice-Hall, Upper Saddle River, NJ, 2000. A good reference for MATLAB usage and the standard scientific computing topics covered in Math 425 (linear algebra, Newton's method, numerical quadrature).


Other books of potential interest (mainly for two-point boundary value problems):

  1. Susanne C. Brenner and L. Ridgway Scott, The Mathematical Theory of Finite Element Methods, Springer-Verlag New York, Inc., New York, 1996. (See chapter 0.)

  2. Gilbert Strang and George J. Fix, An Analysis of the Finite Elmement Method, Wellesley-Cambridge Press, Wellesley, MA, 1997. Originally published by Prentice-Hall in 1973. (See Chapter 1.)

  3. K. Eriksson, D. Estep, P. Hansbo, and C. Johnson, Computational Differential Equations, Cambridge, 1996. (See Part II, Chapter 8.)

  4. Claes Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge, 1987. (See Chapters 1 and 2.)

  5. K.W. Morton and D.F. Mayers, Numerical Solution of Partial Differential Equations, Cambridge, 1994. (See pp. 184-197)

  6. Gene H. Golub and James M. Ortega, Scientific Computing and Differential Equations: An Introduction to Numerical Methods, Academic Press, Boston, 1992. (More geared toward initial value problems for ODE's.)

  7. P.M. Prenter, Splines and Variational Methods, Wiley, 1975. Republished in Wiley Classics Library, 1989. (See chapters 6 and 7.)

  8. Barno Szabo and Ivo Babuska, Finite Element Analysis, Wiley, 1991. (More engineering-oriented.)

  9. O.C. Zienkiewicz, The Finite Element Method in Engineering Science, McGraw-Hill, 1971. (A classic; it has gone through several editions.)