New Primal-Dual Weak Galerkin Finite Element Methods for Convection-Diffusion Problems

Waixiang Cao; Chunmei Wang

doi:10.1016/j.apnum.2020.12.012

New Primal-Dual Weak Galerkin Finite Element Methods for Convection-Diffusion Problems

Waixiang Cao, Chunmei Wang

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

This article devises a new primal-dual weak Galerkin finite element method for the convection-diffusion equation. Optimal order error estimates are established for the primal-dual weak Galerkin approximations in various discrete norms and the standard L² norms. A series of numerical experiments are conducted and reported to verify the theoretical findings.

Original language	English
Pages (from-to)	171-191
Number of pages	21
Journal	Applied Numerical Mathematics
Volume	162
DOIs	https://doi.org/10.1016/j.apnum.2020.12.012
State	Published - Apr 2021

Keywords

Convection-diffusion
Finite element methods
Polygonal or polyhedral meshes
Primal-dual
Weak Galerkin
Weak gradient

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10.1016/j.apnum.2020.12.012

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title = "New Primal-Dual Weak Galerkin Finite Element Methods for Convection-Diffusion Problems",

abstract = "This article devises a new primal-dual weak Galerkin finite element method for the convection-diffusion equation. Optimal order error estimates are established for the primal-dual weak Galerkin approximations in various discrete norms and the standard L2 norms. A series of numerical experiments are conducted and reported to verify the theoretical findings.",

keywords = "Convection-diffusion, Finite element methods, Polygonal or polyhedral meshes, Primal-dual, Weak Galerkin, Weak gradient",

author = "Waixiang Cao and Chunmei Wang",

note = "Funding Information: The research of Waixiang Cao was partially supported by NSFC grant No. 11871106.The research of Chunmei Wang was partially supported by National Science Foundation Award DMS-1849483. Publisher Copyright: {\textcopyright} 2020",

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AU - Cao, Waixiang

AU - Wang, Chunmei

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PY - 2021/4

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N2 - This article devises a new primal-dual weak Galerkin finite element method for the convection-diffusion equation. Optimal order error estimates are established for the primal-dual weak Galerkin approximations in various discrete norms and the standard L2 norms. A series of numerical experiments are conducted and reported to verify the theoretical findings.

AB - This article devises a new primal-dual weak Galerkin finite element method for the convection-diffusion equation. Optimal order error estimates are established for the primal-dual weak Galerkin approximations in various discrete norms and the standard L2 norms. A series of numerical experiments are conducted and reported to verify the theoretical findings.

KW - Convection-diffusion

KW - Finite element methods

KW - Polygonal or polyhedral meshes

KW - Primal-dual

KW - Weak Galerkin

KW - Weak gradient

UR - http://www.scopus.com/inward/record.url?scp=85098170452&partnerID=8YFLogxK

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DO - 10.1016/j.apnum.2020.12.012

M3 - Article

VL - 162

SP - 171

EP - 191

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

New Primal-Dual Weak Galerkin Finite Element Methods for Convection-Diffusion Problems

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Keywords

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