Error estimation for FEM in acoustic scattering: Dedicated to the memory of Prof. dr. habil. inż. Marian Kmiecik - Ihlenburg, Frank (Computer Assisted Methods in Engineering and Science, 1996)
We consider apriori and aposteriori error estimation for the FEM solution of Helmholtz problems that arise in acoustic scattering. Our focus is on the case of high wavenumber (highly oscillatory solutions) where existing asymptotic estimates had to be generalized to "preasymptotic" statements that are applicable in the range of engineering computations. We refer the key results of an 1D analytic study of error behawior (apriori estimates) and announce new results on aposteriori error estimation. Specifically, we show that the standard local aposteriori error indicators are not, in general, reliable for Helmholtz problems with high wave number, due to considerable numerical pollution in the error. We then discuss a methodology how to (aposteriori) estimate, in addition to the local error, the pollution error. Throughout, the theoretical results will be supplemented by numerical evaluation.