Hybrid domain decomposition solvers for scalar and vectorial wave equation

We present hybrid finite element methods, which are equivalent to a discontinuous Galerkin method based on the ultra weak variational formulation (UWVF) by Cessenat and Despres. When solving a scalar or vectorial wave equation with hybrid finite elements, normal and tangential continuity of the flux field, respectively, is broken across element interfaces and reinforced again by introducing hybrid variables, which are supported only on the element facets. Using this technique, coupling between degrees of freedom belonging to the interior of different elements is avoided, and the large number of volume unknowns on the element can be eliminated easily. Consequently, the linear system of equations needs only to be solved for the introduced facet degrees of freedom. It is shown by numerical experiments, that iterative solvers using Schwarz preconditioners show good convergence properties for these systems of equations.