A posteriori error analysis of semilinear parabolic interface problems using elliptic reconstruction. Issue 4 (12th March 2018)

• Record Type: Journal Article
• Authors: Sen Gupta, Jhuma; Sinha, Rajen Kumar
• Is Part Of: Applicable analysis. Volume 97:Issue 4(2018)
• Page Start: 552
• Page End: 570
• Publication Date: 2018-03-12
• Subjects: Semilinear parabolic interface problems -- the backward Euler and Crank-Nicolson approximations -- elliptic reconstruction -- a posteriori error analysis; 65N15 -- 65N30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1277582
• Languages: English
• ISSNs: 0003-6811

Abstract

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.