Convergence analysis of weak Galerkin flux-based mixed finite element method for solving singularly perturbed convection-diffusion-reaction problem
A new weak Galerkin (WG) method is designed and analyzed for solving singularly perturbed (SP)-convection-diffusion-reaction (CDR) problems. It is based on the mixed finite element method (FEM). Due to the fitted operator-type method character, it produces stable approximations on uniform meshes. The method has some special features compared to existing ones: the discontinuous function is used for finite element space, a flux variable is introduced as an auxiliary variable that generates a variational form independent of the primal variable. In this way, the weak Galerkin approximation of the primal variable is obtained by a simple post-processing procedure and approximation of the flux variable. The proposed method is optimally convergent for both approximations of flux and primal variables in the energy norm and the \(L_2\)-norm. Numerical results for test problems with smooth solutions, interior layers with continuous and discontinuous boundary conditions, and for a rotational problem, show that the WG flux-based mixed FEM is an an efficient method for simulating the SP-CDR problems
scientific article; zbMATH DE number 7316850
scientific article