High-order local artificial boundary conditions for problems in unbounded domains

Abstract

In this paper we present error estimates for the finite element approximation of Poisson and modified Helmholtz equations outside an obstacle or in a semi-infinite strip in the plane. The finite element approximation is formulated on a bounded domain using a local approximate artificial boundary condition. In fact there is a sequence of local approximate boundary conditions for a given artificial boundary. Our error estimates are based on the mesh size and the location of the artificial boundary. The numerical stability and robustness of the method are discussed. Numerical experiments are presented to demonstrate the performance of the method and our error estimates.