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Volume 20, Issue 2
Weak Galerkin Finite Element Methods for Parabolic Problems with $L^2$ Initial Data

Naresh Kumar & Bhupen Deka

DOI: 10.4208/ijnam2023-1009

Int. J. Numer. Anal. Mod., 20 (2023), pp. 199-228.

Published online: 2023-01

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  • 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.

  • Keywords

Parabolic equations, weak Galerkin method, non-smooth data, polygonal mesh, optimal $L^2$ error estimates.

  • AMS Subject Headings

65N15, 65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-20-199, author = {Kumar , Naresh and Deka , Bhupen}, title = {Weak Galerkin Finite Element Methods for Parabolic Problems with $L^2$ Initial Data}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2023}, volume = {20}, number = {2}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2023-1009}, url = {http://global-sci.org/intro/article_detail/ijnam/21354.html} }
TY - JOUR T1 - Weak Galerkin Finite Element Methods for Parabolic Problems with $L^2$ Initial Data AU - Kumar , Naresh AU - Deka , Bhupen JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 199 EP - 228 PY - 2023 DA - 2023/01 SN - 20 DO - http://doi.org/10.4208/ijnam2023-1009 UR - https://global-sci.org/intro/article_detail/ijnam/21354.html KW - Parabolic equations, weak Galerkin method, non-smooth data, polygonal mesh, optimal $L^2$ error estimates. AB -

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.

Kumar , Naresh and Deka , Bhupen. (2023). Weak Galerkin Finite Element Methods for Parabolic Problems with $L^2$ Initial Data. International Journal of Numerical Analysis and Modeling. 20 (2). 199-228. doi:10.4208/ijnam2023-1009
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