Weak Galerkin Finite Element Method for Second Order Parabolic Equations

Weak Galerkin Finite Element Method for Second Order Parabolic Equations

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.