Numerical Analysis of PDEs, S.H. Lui, 2011.
Wiley series in Pure and Applied Mathematics (487 pages)

Table of Contents:
1) Finite Difference
2) Mathematical Theory of Elliptic PDEs
3) Finite Elements
4) Numerical Linear Algebra
5) Spectral methods
6) Evolutionary PDEs
7) Multigrid
8) Domain Decomposition
9) Infinite Domains
10) Nonlinear Problems


MATLAB programs
2nd order finite difference 2D Poisson solver (direct and PCG)
1D spectral collocation Poisson solver
1D FFT Dirichlet Poisson solver
1D FFT Neumann Poisson solver
2D Finite element solver