Hybridizing Raviart-Thomas Elements for the Helmholtz Equation

Abstract This article deals with the application of hybridized mixed methods for discretizing the Helmholtz problem, which allows for a fast, iterative solution, from a mixed formulation using Raviart-Thomas finite elements. Two ways of hybridizing the problem are presented, which means breaking the normal continuity of the fluxes and imposing it weakly via functions supported on the element interfaces. The first method is the ultra-weak variational formulation, first introduced by Cessenat and Després (1998); the second one uses Lagrange multipliers. Good behavior of iterative solvers is observed for both methods, as well as for high wave numbers.

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