A Simplified Weak Galerkin Finite Element Method: Algorithm and Error Estimates

In this article a simplified weak Galerkin finite element method is developed for the Dirichlet boundary value problem of convection-diffusion-reaction equations. The simplified weak Galerkin method utilizes only the degrees of freedom on the boundary of each element and, hence, has significantly re...

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Bibliographic Details
Main Authors Liu, Yujie, Wang, Junping
Format Journal Article
LanguageEnglish
Published 26.08.2018
Subjects
Mathematics - Numerical Analysis
Online AccessGet full text
DOI10.48550/arxiv.1808.08667

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Summary:In this article a simplified weak Galerkin finite element method is developed for the Dirichlet boundary value problem of convection-diffusion-reaction equations. The simplified weak Galerkin method utilizes only the degrees of freedom on the boundary of each element and, hence, has significantly reduced computational complexity over the regular weak Galerkin finite element method. A stability and some optimal order error estimates in the$H^1$and$L^2$norms are established for the corresponding numerical solutions. Numerical results are presented to verify the theory error estimates and a superconvergence phenomena on rectangular partitions.
DOI:10.48550/arxiv.1808.08667