New interpolation error estimates and a posteriori error analysis for linear parabolic interface problems |
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Authors: | Jhuma Sen Gupta Rajen Kumar Sinha G Murali Mohan Reddy Jinank Jain |
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Institution: | 1. Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati‐781039, India;2. Department of Applied Mathematics and Statistics, Institute of Mathematics and Computer Sciences, University of S?o Paulo, Sao Carlos, S?o Paulo, Brazil;3. Department of Computer Science and Engineering, Indian Institute of Technology Jodhpur, Rajasthan‐342001, India |
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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 ‐norm and almost optimal order in the ‐norm. The interfaces are assumed to be of arbitrary shape but are smooth for our purpose. Numerical results are presented to validate our derived estimators. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 570–598, 2017 |
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Keywords: | a posteriori error estimates Clé ment‐type interpolation estimates elliptic reconstruction parabolic interface problems |
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