Hybridizing Raviart-thomas Elements for the Helmholtz Equation

This paper deals with the application of hybridized mixed methods for discretizing the Helmholtz problem. Starting from a mixed formulation, where the flux is considered a separate unknown, we use Raviart-Thomas finite elements to approximate the solution. We present two ways of hybridizing the problem, which means breaking the normal continuity of the fluxes and then imposing continuity weakly via functions supported on the element faces or edges. The first method is the Ultra-Weak Variational Formulation, first introduced by Cessenat and Després [7]; the second one uses Lagrange multipliers on element interfaces. We compare the two methods, and give numerical results. We observe that the iterative solvers applied to the two methods behave well for large wave numbers.