A posteriori error analysis of semilinear parabolic interface problems using elliptic reconstruction

摘要

In this article, a posteriorierror analysis for space-time discretizations of semilinear parabolic interface problems in a bounded convex domain in R-2 is presented and analyzed. In time discretizations both the backward Euler and the Crank-Nicolson approximations are considered whereas in space we have considered the standard piecewise linear finite elements. A posteriori error estimates of optimal order in time and almost optimal order in space are derived in the norm. The main technical tools used are the energy argument combined with the elliptic reconstruction technique. The forcing term is assumed to satisfy the Lipschitz condition.