A posteriori error estimation and adaptive finite element computation of the Helmholtz equation in exterior domains

This paper presents adaptive finite element methods for the Helmholtz equation in exterior domains, with application to time-harmonic acoustics problems. Particular focus is given on the a posteriori error estimator, which is an explicit function of residuals and provides an upper bound on the global L(2)-norm of the error. An h-adaptive strategy, which does not require knowledge of the scaling constant appearing in the error estimator, is described. Numerical results for a two-dimensional model problem show that significant problem size reduction can be obtained through this adaptive approach. An algorithm is presented to compute the scaling constant, which leads to computable error estimates. The accuracy of the error estimates, indicated by the global effectivity index, varies with the wave number.