Error Estimator Using Higher Order FEM for an Interface Problem

Abstract

A higher order finite element method is considered to treat an interface problem. The polynomial degree is allowed to be arbitrary but it is fixed for the FEM-variational formulation. We propose an error estimator which turns out to be efficient and reliable. We demonstrate upper and lower bounds of the error estimator with respect to the exact accuracy. For the transmission problem, the coefficients for the internal and external domains can be highly dissimilar. One major difficulty is the characteristic of the estimator at the interface. The a-posteriori error estimates can be computed very efficiently element by element. To corroborate the theoretical analysis, we report on a few numerical results.