Mixed Discontinuous Galerkin Approximation of the Maxwell Operator: Non-Stabilized Formulation

A non-stabilized mixed discontinuous Galerkin method for the discretization of the Maxwell operator on simplicial meshes is studied. In contrast to the stabilized scheme introduced in [7], the proposed formulation contains no normal– jump stabilization; instead, it is based on discontinuous mixed-order (P) − P elements for the approximation of the unknowns. A priori error bounds in the energy norm are derived that show convergence rates of the order O(h) in the mesh size h. The error analysis relies on suitable decompositions of discontinuous spaces and on stability properties of the underlying conforming spaces. The formulation is tested on a set of numerical examples in two space dimensions.