Convergence analysis of weak Galerkin flux-based mixed finite element method for solving singularly perturbed convection-diffusion-reaction problem

This article is assigned to the numerical analysis of a new weak Galerkin mixed-type finite element method for the diffusion-convection-reaction problem with singular perturbation. The variational form of the considered method compared to the existing methods consists of a single variational equation, where flux is the only unknown. Hence it is sufficient to provide a weak Galerkin approximation for the flux variable, and immediately approximation of the primal unknown can be obtained by a post-processing strategy. We prove the well-posedness, stability and convergence of the weak Galerkin scheme. Eventually, some numerical experiments to support the nice efficiency of the technique and analytical results are presented. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.

Automated summary

This article presents a new weak Galerkin mixed-type finite element method for the diffusion-convection-reaction problem with singular perturbation. By providing a weak Galerkin approximation for the flux, an approximation of the primal unknown can be obtained immediately, and the well-posedness, stability, and convergence of the scheme are proven. Numerical experiments are also conducted to support the efficiency of the technique and analytical results.