A Stabilizer Free Weak Galerkin Finite Element Method for General Second-Order Elliptic Problem

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.