[jedbrown]

Hmm, I can't think of a single general book that could be considered general CS&E. There are many great books in, e.g. numerical linear algebra, domain decomposition methods, finite element or finite volume methods, etc. While these are quite valuable, I never felt like they really changed my perspective on the field. So instead, here are some less conventional starting points.

Any talk by David Keyes. This one is mostly directed towards a physics audience (it's not specifically about ice sheets). http://www.columbia.edu/~kd2112/IceSheets09.pdf

This one is directed at a computing audience http://www.cespr.fsu.edu/lighthill/keyes_publiclecture.pdf (http://www.youtube.com/watch?v=RYxNVX9SYtk (skip ahead a few minutes to skip the introduction)).

This review paper has more background from an implicit solvers perspective and lots of citations for more background. http://www.cs.odu.edu/~keyes/papers/jfnk.pdf

An open source library. I learned a lot from experimenting with methods and reading PETSc source code. (And soon started developing the library too.) http://mcs.anl.gov/petsc

Algorithms like multigrid, fast multipole, and WENO that are unreasonably better than naive alternatives (for appropriate problems).

Note: CS&E is significantly bigger than partial differential equations, but PDEs are still a very central component.