Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Part I

Three Galerkin methods using discontinuous approximation spaces are introdu ced to solve elliptic problems. The underlying bilinear form for all three methods is the same and is nonsymmetric. In one case, a penalty is added to the form and in another, a constraint on jumps on each face of the triangu lation. All three methods are locally conservative and the third one is not restricted. Optimal a priori hp error estimates are derived for all three procedures.