On a Posteriori Error Bound for Weak Galerkin Finite Element Method for Semilinear Parabolic Problems
Authors
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Department of Mathematics, BITS Pilani Hyderabad, Hyderabad - 500078 ,IN
P. V. Anjali -
Department of Mathematics, BITS Pilani Hyderabad, Hyderabad - 500078 ,INAmit Kumar Pal
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Department of Mathematics, BITS Pilani Hyderabad, Hyderabad - 500078 ,INJhuma Sen Gupta
DOI:
https://doi.org/10.18311/jims/2024/32085Keywords:
Weak Galerkin Finite Element Method, Weak Gradient, Posteriori Error Analysis, Semilinear Parabolic Problems, Fully Discrete Finite Element Approximation.Abstract
This article presents a posteriori error analysis for the weak Galerkin finite element method based on the backward Euler approximation for semilinear parabolic problems in a bounded convex polygonal domain in R2 . An optimal order a posteriori error bound is obtained with respect to the L2 -norm in time and in the energy norm in space for the fully discrete backward Euler weak Galerkin finite element method for semilinear parabolic problems. We have exploited the elliptic reconstruction technique combined with the energy arguments to derive error bound. The source term is assumed to satisfy the Lipschitz condition. Numerical results are reported to validate the asymptotic behaviour of the derived error estimators.
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Copyright (c) 2024 Jhuma Sen Gupta, Anjali
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2023-10-03
Published 2024-07-01
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