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.
Acknowledgements
The authors wish to thank both the reviewers for their valuable comments and suggestions on this manuscript.
Notes
No potential conflict of interest was reported by the authors.