General Texts in Numerical Analysis

K. Atkinson: An Introduction to Numerical Analysis, Wiley, (2nd ed.), 1989.
P.G. Ciarlet and J. L. Lions (eds), Handbook of Numerical Analysis,
     North Holland, 1990.
S. Conte and C. de Boor: Elementary Numerical Analysis, McGraw-Hill, 1980. 
G. Dahlquist and A. Bjorck: Numerical Methods, Prentice Hall, 1974.
W. Gautschi: Numerical Analysis: an introduction, Birkhauser, 1997.
E. Isaacson and H. Keller: Analysis of Numerical Methods, Wiley, 1966
     (or Dover 1994).
D. Kahaner, C. Moler, and S. Nash: Numerical Methods and Software,
     Prentice-Hall, 1989.
D. Kincaid and W. Cheney: Numerical Analysis: Mathematics of Scientific
     Computing, Brooks/Cole, 1996.
A. Ralston and P. Rabinowitz: A First Course in Numerical Analysis, 
     McGraw-Hill, 1978.
L. Shampine, Allen, and Pruess: Fundamentals of Numerical Computing,
G. W. Stewart: Afternotes on Numerical Analysis, SIAM, 1996.
G. W. Stewart: Afternotes goes to Graduate School Lectures on Advanced
     Numerical Analysis, SIAM, 1998.
J. Stoer and R. Bulirsch: Introduction to Numerical Analysis, Springer-Verlag,

Finite Element Method

O. Axelsson and V.A. Barker: Finite element solution of boundary value
     problems: theory and computation, Academic Press, 1984.
R. E. Bank: PLTMG A Software Package for Solving Elliptic Partial
     Differential Equations User's Guide 8.0, SIAM 1998.
M. Bernadou: Finite Element Methods for Thin Shell Problems, John Wiley,
D. Braess: Finite Elements: Theory, fast solvers, and applications in
     solid mechanics, Cambridge University Press, 1997.
S. Brenner and L. R. Scott: The Mathematical Theory of Finite Element
     Methods, Springer-Verlag, 1994.
F. Brezzi and M. Fortin: Mixed and Hybrid Finite Element Methods,
     Springer-Verlag, 1991.
P. G. Ciarlet:  The Finite Element Method for Elliptic Problems,
     North Holland, 1980.
P. G. Ciarlet and J. L. Lions (eds): Handbook of Numerical Analysis, Volumes
     I-VI, Elsevier.
K. Eriksson, D. Estep, P. Hansbo, C. Johnson: Computational Differential
     Equations, Cambridge University Press, 1996.
V. A. Girault and P-A. Raviart: Finite Element Methods for Navier-Stokes
     Equations, Springer-Verlag, 1986.
M. Gunzburger, Finite Element Methods for Viscous Incompressible Flows,
     Academic Press, 1989.
T. J. R. Hughes, The Finite Element Method: Linear Static and Dynamic
     Finite Element Analysis, Prentice Hall, 1987.
C. Johnson: Numerical Solutions of Partial Differential Equations by
     the Finite Element Method, Cambridge University Press, 1987.
G. Strang and G. Fix: An Analysis of the Finite Element Method,
     Prentice-Hall, 1973.
B. Szab\'o and I. Babu\u ska: Finite Element Analysis
O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method
     (4th edition), McGraw Hill, 1989.

Finite Difference Methods for Partial Differential Equations

S. K. Godunov and V. S. Ryabenki, Difference Schemes: an introduction
     to the underlying theory, North Holland, 1987.
B. Gustafsson, H-O. Kreiss, and J. Oliger, Time dependent problems and
     difference methods, Wiley, 1995.
C. Hall and T. Porsching: Numerical Analysis of Partial Differential
     Equations, Prentice Hall, 1990.
R. J. LeVeque, Numerical methods for conservation laws, Birkhauser Verlag,
I. Iserles, A First Course in the Numerical Analysis of Differential
     Equations, Cambridge University Press, 1996.
A. Quarteroni and A. Valli, Numerical approximation of partial differential
     equations,      Springer-Verlag, 1994.
R. D. Richtmyer and K. W. Morton:  Difference Methods for Initial Value
     Problems, Wiley-Interscience, 1967.
G. Sod: Numerical Methods in Fluid Mechanics: Initial and
     Initial Boundary Value Problems, Cambridge University Press, 1985.
J. Strikwerda: Finite Difference Schemes and Partial Differential
     Equations, Wadsworth and Brooks/Cole, 1989.
J. W. Thomas, Numerical Partial Differential Equations: Finite Difference
Methods, Springer-Verlag, 1995.

Multigrid and Domain Decomposition

J. H. Bramble: Multigrid methods, Pitman, 1993.
W. L. Briggs: A Multigrid Tutorial, SIAM, 1987.
W. Hackbusch: Multi-Grid Methods and Applications, Springer-Verlag, 1986.
B. Smith, P. Bjorstad, and W. Gropp: Domain Decomposition, Cambridge
     University Press, 1996.
J. Xu: Iterative methods by space decomposition and subspace corrections,
     SIAM Review 34 (1992), 581-613.