ADAPTIVE FINITE-ELEMENTS FOR EXTERIOR DOMAIN PROBLEMS

We present an adaptive finite element method for solving elliptic prob lems in exterior domains, that is for problems in the exterior of a bo unded closed domain in R-d,, d is an element of {2, 3}. We describe a procedure to generate a sequence of bounded computational domains Omeg a(h)(k), k = 1, 2, ..., more precisely, a sequence of successively fin er and larger grids, until the desired accuracy of the solution u(h) i s reached. To this end we prove an a posteriori error estimate for the error on the unbounded domain in the energy norm by means of a residu al based error estimator. Furthermore we prove convergence of the adap tive algorithm. Numerical examples show the optimal order of convergen ce. Mathematics Subject Classification (1991): 65N15, 65N30, 65N50.