Year: 2023
Author: Naresh Kumar, Bhupen Deka
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 2 : pp. 199–228
Abstract
We analyze the weak Galerkin finite element methods for second-order linear parabolic problems with $L^2$ initial data, both in a spatially semidiscrete case and in a fully discrete case based on the backward Euler method. We have established optimal $L^2$ error estimates of order $O(h^2/t)$ for semidiscrete scheme. Subsequently, the results are extended for fully discrete scheme. The error analysis has been carried out on polygonal meshes for discontinuous piecewise polynomials in finite element partitions. Finally, numerical experiments confirm our theoretical convergence results and efficiency of the scheme.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2023-1009
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 2 : pp. 199–228
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Parabolic equations weak Galerkin method non-smooth data polygonal mesh optimal $L^2$ error estimates.