Check out the current release of the
Incompressible Flow & Iterative Solver Software (IFISS)
Matlab and Octave toolbox.
This open source
software package is associated with the second edition of
Finite Elements and Fast Iterative Solvers
with applications in incompressible fluid dynamics.
Check out our highly-regarded (SUMS) textbook on Essential PDEs using Amazon books.
A gentle introduction
to the mathematics underlying finite element convergence theory can
be found in the
Finite Element Primer.
My lecture notes on
finite element approximation
may also be of interest.