  In this paper we present and implement the Palindromic Discontinuous Galerkin
(PDG) method in dimensions higher than one. The method has already been exposed
and tested in [4] in the one-dimensional context. The PDG method is a general
implicit high order method for approximating systems of conservation laws. It
relies on a kinetic interpretation of the conservation laws containing stiff
relaxation terms. The kinetic system is approximated with an
asymptotic-preserving high order DG method. We describe the parallel
implementation of the method, based on the StarPU runtime library. Then we
apply it on preliminary test cases.
