The solution of the Poisson equation using P1 Finite Elements on
different adaptive even non-conforming grids can be found
here.
Discontinous Galerkin Methods for Convection Dominated Problems
Here we consider a stabilized Discontinuous Galerkin (DG) method for
hyperbolic and convection dominated problems. The presented scheme can
be used in several space dimensions and with a wide range of grid
element types for locally adaptive and load balanced
parallel computations. More details about the scheme can be found here.