Weak Galerkin Finite Element Methods for Parabolic Problems with $L^2$ Initial Data

Weak Galerkin Finite Element Methods for Parabolic Problems with $L^2$ Initial Data

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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.

Author Details

Naresh Kumar

Bhupen Deka