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 - <p style="text-align: justify;">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&nbsp;$\mathcal{O}(h^{k+1})$ 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.</p>