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Volume 13, Issue 4
Weak Galerkin Finite Element Method for Second Order Parabolic Equations

H.-Q. Zhang, Y.-K. Zou, Y.-X. Xu, Q.-L. Zhai & H. Yue

Int. J. Numer. Anal. Mod., 13 (2016), pp. 525-544.

Published online: 2016-07

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  • 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.

  • Keywords

Weak Galerkin finite element methods, discrete gradient, parabolic equations.

  • AMS Subject Headings

65M60, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-13-525, author = {H.-Q. Zhang, Y.-K. Zou, Y.-X. Xu, Q.-L. Zhai and H. Yue}, title = {Weak Galerkin Finite Element Method for Second Order Parabolic Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/451.html} }
TY - JOUR T1 - Weak Galerkin Finite Element Method for Second Order Parabolic Equations AU - H.-Q. Zhang, Y.-K. Zou, Y.-X. Xu, Q.-L. Zhai & H. Yue JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 525 EP - 544 PY - 2016 DA - 2016/07 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/451.html KW - Weak Galerkin finite element methods, discrete gradient, parabolic equations. AB -

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.

H.-Q. Zhang, Y.-K. Zou, Y.-X. Xu, Q.-L. Zhai and H. Yue. (2016). Weak Galerkin Finite Element Method for Second Order Parabolic Equations. International Journal of Numerical Analysis and Modeling. 13 (4). 525-544. doi:
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