Year: 2021
Author: Ahmed AL-Taweel, Saqib Hussain, Runchang Lin, Peng Zhu
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2021-IJNAM-18725
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 3 : pp. 311–323
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Stabilizer free weak Galerkin methods weak Galerkin finite element methods weak gradient error estimates.