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

Ahmed Al-Taweel, Saqib Hussain, Runchang Lin & Peng Zhu

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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COPYRIGHT: © Global Science Press

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@Article{IJNAM-18-311, author = {Al-Taweel , Ahmed and Hussain , Saqib and Lin , Runchang and Zhu , Peng}, 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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