Preprint 05-2015

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

Author(s) : Kersten Schmidt , Julien Diaz, Christian Heier

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 05-2015

MSC 2000

65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Abstract :
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.

Keywords : Interior Penalty Galerkin finite element method, Local absorbing boundary condition