Convergence analysis of weak Galerkin flux-based mixed finite element method for solving singularly perturbed convection-diffusion-reaction problem
type: Item
instance of: scholarly article
title: Convergence analysis of weak Galerkin flux-based mixed finite element method for solving singularly perturbed convection-diffusion-reaction problem
zbMATH Open document ID: 1459.65221
author: Zeinab Gharibi
author: Mehdi Dehghan
published in: Applied Numerical Mathematics
publication date: 2021-03-02T00:00:00Z
review text: 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
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A02
Mathematics Subject Classification ID: 76U05
zbMATH DE Number: 7316850
zbMATH Keywords: convection-diffusion-reaction model
zbMATH Keywords: weak Galerkin method
zbMATH Keywords: mixed finite element method
zbMATH Keywords: singularly perturbed PDEs
zbMATH Keywords: well-posedness
zbMATH Keywords: convergence and stability
zbMATH Keywords: turbulence parameter
reviewed by: Bülent Karasözen
MaRDI profile type: Publication
full work available at URL: j.apnum.2021.01.016
OpenAlex ID: W3126463413
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DOI: 10.1016/J.APNUM.2021.01.016
description: scientific article; zbMATH DE number 7316850