A Conforming Discontinuous Galerkin Finite Element Method for Second-Order Parabolic Equation
Year: 2025
Author: Fuchang Huo, Yuchen Sun, Jiageng Wu, Liyuan Zhang
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 3 : pp. 432–458
Abstract
The conforming discontinuous Galerkin (CDG) finite element method is an innovative and effective numerical approach to solve partial differential equations. The CDG method is based on the weak Galerkin (WG) finite element method, and removes the stabilizer in the numerical scheme. And the CDG method uses the average of the interior function to replace the value of the boundary function in the standard WG method. The integration by parts is used to construct the discrete weak gradient operator in the CDG method. This paper uses the CDG method to solve the parabolic equation. Firstly, the semi-discrete and full-discrete numerical schemes of the parabolic equation and the well-posedness of the numerical methods are presented. Then, the corresponding error equations for both numerical schemes are established, and the optimal order error estimates of H1 and L2 are provided, respectively. Finally, the numerical results of the CDG method are verified.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2025-1019
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 3 : pp. 432–458
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Conforming discontinuous Galerkin finite element method parabolic equation weak Galerkin finite element method optimal order convergence.
Author Details
Fuchang Huo Email
Yuchen Sun Email
Jiageng Wu Email
Liyuan Zhang Email