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Volume 22, Issue 2
Weak Galerkin Finite Element Method Based on POD for Nonlinear Parabolic Equations

Jianghong Zhang, Fuzheng Gao & Jintao Cui

DOI: 10.4208/ijnam2025-1008

Int. J. Numer. Anal. Mod., 22 (2025), pp. 157-177.

Published online: 2025-02

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  • Abstract

In this paper, we establish a novel reduced-order weak Galerkin (ROWG) finite element method for solving parabolic equation with nonlinear compression coefficient. We first present the classical weak Galerkin finite element discretization scheme and derive the optimal error estimates. Then we apply a proper orthogonal decomposition (POD) technique to develop the ROWG method, which can effectively reduce degrees of freedom and CPU time. The optimal order error estimates are also derived, and the algorithm flow is provided. Finally, some numerical experiments illustrate the performance of the ROWG method. The numerical results show that the proposed ROWG method is efficient for solving nonlinear parabolic equations.

  • Keywords

Weak Galerkin finite element method, nonlinear parabolic equations, proper orthogonal decomposition.

  • AMS Subject Headings

78M10

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-22-157, author = {Zhang , JianghongGao , Fuzheng and Cui , Jintao}, title = {Weak Galerkin Finite Element Method Based on POD for Nonlinear Parabolic Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2025}, volume = {22}, number = {2}, pages = {157--177}, abstract = {

In this paper, we establish a novel reduced-order weak Galerkin (ROWG) finite element method for solving parabolic equation with nonlinear compression coefficient. We first present the classical weak Galerkin finite element discretization scheme and derive the optimal error estimates. Then we apply a proper orthogonal decomposition (POD) technique to develop the ROWG method, which can effectively reduce degrees of freedom and CPU time. The optimal order error estimates are also derived, and the algorithm flow is provided. Finally, some numerical experiments illustrate the performance of the ROWG method. The numerical results show that the proposed ROWG method is efficient for solving nonlinear parabolic equations.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2025-1008}, url = {http://global-sci.org/intro/article_detail/ijnam/23819.html} }
TY - JOUR T1 - Weak Galerkin Finite Element Method Based on POD for Nonlinear Parabolic Equations AU - Zhang , Jianghong AU - Gao , Fuzheng AU - Cui , Jintao JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 157 EP - 177 PY - 2025 DA - 2025/02 SN - 22 DO - http://doi.org/10.4208/ijnam2025-1008 UR - https://global-sci.org/intro/article_detail/ijnam/23819.html KW - Weak Galerkin finite element method, nonlinear parabolic equations, proper orthogonal decomposition. AB -

In this paper, we establish a novel reduced-order weak Galerkin (ROWG) finite element method for solving parabolic equation with nonlinear compression coefficient. We first present the classical weak Galerkin finite element discretization scheme and derive the optimal error estimates. Then we apply a proper orthogonal decomposition (POD) technique to develop the ROWG method, which can effectively reduce degrees of freedom and CPU time. The optimal order error estimates are also derived, and the algorithm flow is provided. Finally, some numerical experiments illustrate the performance of the ROWG method. The numerical results show that the proposed ROWG method is efficient for solving nonlinear parabolic equations.

Zhang , JianghongGao , Fuzheng and Cui , Jintao. (2025). Weak Galerkin Finite Element Method Based on POD for Nonlinear Parabolic Equations. International Journal of Numerical Analysis and Modeling. 22 (2). 157-177. doi:10.4208/ijnam2025-1008
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