Volume 18, Issue 3
A Stabilizer Free Weak Galerkin Finite Element Method for General Second-Order Elliptic Problem

Int. J. Numer. Anal. Mod., 18 (2021), pp. 311-323.

Published online: 2021-03

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• Abstract

This paper proposes a stabilizer free weak Galerkin (SFWG) finite element method for the convection-diffusion-reaction equation in the diffusion-dominated regime. The object of using the SFWG method is to obtain a simple formulation which makes the SFWG algorithm (9) more efficient and the numerical programming easier. The optimal rates of convergence of numerical errors of $\mathcal{O}(h^k)$ in $H^1$ and $\mathcal{O}(h^{k+1})$ in $L^2$ norms are achieved under conditions $( P_k(K), P_k(e), [P_j (K)]^2 )$ , $j = k + 1$, $k = 1, 2$ finite element spaces. Numerical experiments are reported to verify the accuracy and efficiency of the SFWG method.

• Keywords

Stabilizer free weak Galerkin methods, weak Galerkin finite element methods, weak gradient, error estimates.

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@Article{IJNAM-18-311, author = {Ahmed and Al-Taweel and and 14628 and and Ahmed Al-Taweel and Saqib and Hussain and and 14629 and and Saqib Hussain and Runchang and Lin and and 14630 and and Runchang Lin and Peng and Zhu and and 14631 and and Peng Zhu}, title = {A Stabilizer Free Weak Galerkin Finite Element Method for General Second-Order Elliptic Problem}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2021}, volume = {18}, number = {3}, pages = {311--323}, abstract = {

This paper proposes a stabilizer free weak Galerkin (SFWG) finite element method for the convection-diffusion-reaction equation in the diffusion-dominated regime. The object of using the SFWG method is to obtain a simple formulation which makes the SFWG algorithm (9) more efficient and the numerical programming easier. The optimal rates of convergence of numerical errors of $\mathcal{O}(h^k)$ in $H^1$ and $\mathcal{O}(h^{k+1})$ in $L^2$ norms are achieved under conditions $( P_k(K), P_k(e), [P_j (K)]^2 )$ , $j = k + 1$, $k = 1, 2$ finite element spaces. Numerical experiments are reported to verify the accuracy and efficiency of the SFWG method.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/18725.html} }
TY - JOUR T1 - A Stabilizer Free Weak Galerkin Finite Element Method for General Second-Order Elliptic Problem AU - Al-Taweel , Ahmed AU - Hussain , Saqib AU - Lin , Runchang AU - Zhu , Peng JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 311 EP - 323 PY - 2021 DA - 2021/03 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/18725.html KW - Stabilizer free weak Galerkin methods, weak Galerkin finite element methods, weak gradient, error estimates. AB -

This paper proposes a stabilizer free weak Galerkin (SFWG) finite element method for the convection-diffusion-reaction equation in the diffusion-dominated regime. The object of using the SFWG method is to obtain a simple formulation which makes the SFWG algorithm (9) more efficient and the numerical programming easier. The optimal rates of convergence of numerical errors of $\mathcal{O}(h^k)$ in $H^1$ and $\mathcal{O}(h^{k+1})$ in $L^2$ norms are achieved under conditions $( P_k(K), P_k(e), [P_j (K)]^2 )$ , $j = k + 1$, $k = 1, 2$ finite element spaces. Numerical experiments are reported to verify the accuracy and efficiency of the SFWG method.

Ahmed Al-Taweel, Saqib Hussain, Runchang Lin & Peng Zhu. (2021). A Stabilizer Free Weak Galerkin Finite Element Method for General Second-Order Elliptic Problem. International Journal of Numerical Analysis and Modeling. 18 (3). 311-323. doi:
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