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

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.

Keywords:

• Semilinear parabolic interface problems
• the backward Euler and Crank-Nicolson approximations
• elliptic reconstruction
• a posteriori error analysis

AMS Subject Classifications:

• 65N15
• 65N30

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.