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

In this paper we present error estimates for the finite element approximati on of Poisson and modified Helmholtz equations outside an obstacle or in a semi-infinite strip in the plane. The finite element approximation is formu lated on a bounded domain using a local approximate artificial boundary con dition. In fact there is a sequence of local approximate boundary condition s for a given artificial boundary. Our error estimates are based on the mes h size and the location of the artificial boundary. The numerical stability and robustness of the method are discussed. Numerical experiments are pres ented to demonstrate the performance of the method and our error estimates. (C) 2000 Elsevier Science S.A. All rights reserved.