A posteriori error analysis of semilinear parabolic interface problems using elliptic reconstruction. Issue 4 (12th March 2018) - Sen Gupta, Jhuma
Abstract : In this article, a posteriori error analysis for space-time discretizations of semilinear parabolic interface problems in a bounded convex domain in 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.