Year: 2016
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 4 : pp. 525–544
Abstract
We apply in this paper the weak Galerkin method to the second order parabolic differential equations based on a discrete weak gradient operator. We establish both the continuous time and the discrete time weak Galerkin finite element schemes, which allow using the totally discrete functions in approximation space and the finite element partitions of arbitrary polygons with certain shape regularity. We show as well that the continuous time weak Galerkin finite element method preserves the energy conservation law. The optimal convergence order estimates in both $H^1$ and $L^2$ norms are obtained. Numerical experiments are performed to confirm the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-IJNAM-451
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 4 : pp. 525–544
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Weak Galerkin finite element methods discrete gradient parabolic equations.