Volume 17, Issue 4
Numerical Investigation on Weak Galerkin Finite Elements

Junping Wang, Xiu YeShangyou Zhang

Int. J. Numer. Anal. Mod., 17 (2020), pp. 517-531.

Published online: 2020-08

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  • Abstract

The weak Galerkin (WG) finite element method is an effective and robust numerical technique for the approximate solution of partial differential equations. The essence of the method is the use of weak finite element functions and their weak derivatives computed with a framework that mimics the distribution or generalized functions. Weak functions and their weak derivatives can be constructed by using polynomials of arbitrary degrees; each chosen combination of polynomial subspaces generates a particular set of weak Galerkin finite elements in application to PDE solving. This article explores the computational performance of various weak Galerkin finite elements in terms of stability, convergence, and supercloseness when applied to the model Dirichlet boundary value problem for a second order elliptic equation. The numerical results are illustrated in 31 tables, which serve two purposes: (1) they provide detailed and specific guidance on the numerical performance of a large class of WG elements, and (2) the information shown in the tables may open new research projects for interested researchers as they interpret the results from their own perspectives.

  • Keywords

Weak Galerkin, finite element methods, weak gradient, second-order elliptic problems, stabilizer-free.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-17-517, author = {Wang , Junping and Ye , Xiu and Zhang , Shangyou}, title = {Numerical Investigation on Weak Galerkin Finite Elements}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {4}, pages = {517--531}, abstract = {

The weak Galerkin (WG) finite element method is an effective and robust numerical technique for the approximate solution of partial differential equations. The essence of the method is the use of weak finite element functions and their weak derivatives computed with a framework that mimics the distribution or generalized functions. Weak functions and their weak derivatives can be constructed by using polynomials of arbitrary degrees; each chosen combination of polynomial subspaces generates a particular set of weak Galerkin finite elements in application to PDE solving. This article explores the computational performance of various weak Galerkin finite elements in terms of stability, convergence, and supercloseness when applied to the model Dirichlet boundary value problem for a second order elliptic equation. The numerical results are illustrated in 31 tables, which serve two purposes: (1) they provide detailed and specific guidance on the numerical performance of a large class of WG elements, and (2) the information shown in the tables may open new research projects for interested researchers as they interpret the results from their own perspectives.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/17867.html} }
TY - JOUR T1 - Numerical Investigation on Weak Galerkin Finite Elements AU - Wang , Junping AU - Ye , Xiu AU - Zhang , Shangyou JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 517 EP - 531 PY - 2020 DA - 2020/08 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/17867.html KW - Weak Galerkin, finite element methods, weak gradient, second-order elliptic problems, stabilizer-free. AB -

The weak Galerkin (WG) finite element method is an effective and robust numerical technique for the approximate solution of partial differential equations. The essence of the method is the use of weak finite element functions and their weak derivatives computed with a framework that mimics the distribution or generalized functions. Weak functions and their weak derivatives can be constructed by using polynomials of arbitrary degrees; each chosen combination of polynomial subspaces generates a particular set of weak Galerkin finite elements in application to PDE solving. This article explores the computational performance of various weak Galerkin finite elements in terms of stability, convergence, and supercloseness when applied to the model Dirichlet boundary value problem for a second order elliptic equation. The numerical results are illustrated in 31 tables, which serve two purposes: (1) they provide detailed and specific guidance on the numerical performance of a large class of WG elements, and (2) the information shown in the tables may open new research projects for interested researchers as they interpret the results from their own perspectives.

Junping Wang, Xiu Ye & Shangyou Zhang. (2020). Numerical Investigation on Weak Galerkin Finite Elements. International Journal of Numerical Analysis and Modeling. 17 (4). 517-531. doi:
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