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- Title
New interpolation error estimates and a posteriori error analysis for linear parabolic interface problems.
- Authors
Sen Gupta, Jhuma; Sinha, Rajen Kumar; Reddy, G. Murali Mohan; Jain, Jinank
- Abstract
We derive residual-based a posteriori error estimates of finite element method for linear parabolic interface problems in a two-dimensional convex polygonal domain. Both spatially discrete and fully discrete approximations are analyzed. While the space discretization uses finite element spaces that are allowed to change in time, the time discretization is based on the backward Euler approximation. The main ingredients used in deriving a posteriori estimates are new Clément type interpolation estimates and an appropriate adaptation of the elliptic reconstruction technique introduced by (Makridakis and Nochetto, SIAM J Numer Anal 4 (2003), 1585-1594). We use only an energy argument to establish a posteriori error estimates with optimal order convergence in the
- Subjects
ERRORS; ESTIMATION theory; FINITE element method; INTERPOLATION; PARABOLA
- Publication
Numerical Methods for Partial Differential Equations, 2017, Vol 33, Issue 2, p570
- ISSN
0749-159X
- Publication type
Article
- DOI
10.1002/num.22120