A stabilizer-free weak Galerkin finite element method on polytopal meshes

A stabilizing/penalty term is often used in finite element methods with discontinuous approximations to enforce connection of discontinuous functions across element boundaries. Removing stabilizers from discontinuous Galerkin finite element methods will simplify formulations and reduce programming c...

Full description

Saved in:
Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 371; p. 112699
Main Authors Ye, Xiu, Zhang, Shangyou
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.06.2020
Subjects
Finite element methods
Polyhedral meshes
Second-order elliptic problems
Weak Galerkin
Weak gradient
secondary
Weak gradient
Polyhedral meshes
Second-order elliptic problems
Weak Galerkin
Finite element methods
primary
Online AccessGet full text
ISSN0377-0427
1879-1778
DOI10.1016/j.cam.2019.112699

Cover

More Information
Summary:A stabilizing/penalty term is often used in finite element methods with discontinuous approximations to enforce connection of discontinuous functions across element boundaries. Removing stabilizers from discontinuous Galerkin finite element methods will simplify formulations and reduce programming complexity significantly. The goal of this paper is to introduce a stabilizer free weak Galerkin (WG) finite element method for second order elliptic equations on polytopal meshes. This new WG method keeps a simple symmetric positive definite form and can work on polygonal/polyhedral meshes. Optimal order error estimates are established for the corresponding WG approximations in both a discrete H1 norm and the L2 norm. Numerical results are presented verifying the theorem.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2019.112699