Abstract
This paper considers a stabilizer-free weak Galerkin (SFWG) finite element method for the time-dependent convection diffusion reaction equation. We describe error estimate for both semidiscrete and fully discrete schemes and achieve the supercloseness convergence rate, which is two orders higher than the optimal order associated with SFWG finite element space (Pk(K),Pk+1(∂K),[Pk+1(K)]2). More precisely, we obtain O(hk+2+τ2) in L∞(H1) norm and O(hk+3+τ2) in L∞(L2) norm. Numerous numerical examples are provided to confirm the theoretical findings and efficiency of the proposed method.
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