An adaptive finite element method for parabolic interface problems with nonzero flux jumps

Abstract

We consider an adaptive finite element method for solving parabolic interface problems with nonzero flux jumps in a two-dimensional convex polygonal domain. We use continuous, piecewise linear functions for the approximation of the spatial variable whereas the backward Euler method is employed for the time discretization. The reliability bound of the estimator is derived in terms of the error indicators using the energy argument. An efficiency bound for the local error in terms of the space error indicator is also established. We provide an adaptive algorithm which reduces the error indicators below any given tolerance within a finite number of steps. Our numerical experiment reveals the performance of the derived error indicators with satisfactory numerical results.