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Non-conforming Galerkin finite element method for symmetric local absorbing boundary conditions

Schmidt, Kersten; Diaz, Julien; Heier, Christian

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

We propose a new solution methodology to incorporate symmetric local absorbing boundary conditions involving higher tangential derivatives into a finite element method for solving the 2D Helmholtz equations. The main feature of the method is that it does not requires the introduction of auxiliary variable nor the use of basis functions of higher regularity on the artificial boundary. The originality lies in the combination of C^0 continuous finite element spaces for the discretization of second order operators with discontinuous Galerkin-like bilinear forms for the discretization of differential operators of order four and above. The method proves to limit the computational costs than methods based on auxiliary variables as soon as the order of the absorbing boundary condition is greater than three or the order of the numerical scheme is greater than two. The article includes the numerical analysis of the discrete discontinuous Galerkin variational formulation. Numerical results show that the method does not hamper the order of convergence of the finite element method, if the polynomial degree on the boundary is sufficiently high.