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The main goal of this article is to investigate the capability of fictitious domain methods to simulate the scattering of linear waves by an obstacle whose shape does not fit the mesh. The space-time discretization relies on a combination of a mixed finite element method µa la Raviart-Thomas with a fairly standard finite difference scheme for the time discretization. The numerical results described in the article point to a good performance of the numerical method investigated here.

Solution of a Wave Equation by a Mixed Finite Element - Fictitious Domain Method