A recovery-based a posteriori error estimator of the weak Galerkin finite element method for elliptic problems

Ying Liu; Gang Wang; Mengyao Wu; Yufeng Nie

doi:10.1016/j.cam.2021.113926

A recovery-based a posteriori error estimator of the weak Galerkin finite element method for elliptic problems

Ying Liu, Gang Wang, Mengyao Wu, Yufeng Nie

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

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

4 Scopus citations

Abstract

In this paper, we propose a recovery-type a posteriori error estimator of the weak Galerkin finite element method for the second order elliptic equation. The reliability and efficiency of the estimator are analyzed by a discrete H¹-norm of the exact error. The estimator is further used in the adaptive weak Galerkin algorithm on the triangular, quadrilateral and other polygonal meshes. Numerical results are provided to demonstrate the effectiveness of the adaptive mesh refinement guided by this estimator.

Original language	English
Article number	113926
Journal	Journal of Computational and Applied Mathematics
Volume	406
DOIs	https://doi.org/10.1016/j.cam.2021.113926
State	Published - 1 May 2022

Keywords

A posteriori error estimator
Adaptive algorithm
Weak Galerkin finite element method
Weak gradient recovery

Access to Document

10.1016/j.cam.2021.113926

Cite this

@article{9a8425728cbf4fe3b0de566004674b21,

title = "A recovery-based a posteriori error estimator of the weak Galerkin finite element method for elliptic problems",

abstract = "In this paper, we propose a recovery-type a posteriori error estimator of the weak Galerkin finite element method for the second order elliptic equation. The reliability and efficiency of the estimator are analyzed by a discrete H1-norm of the exact error. The estimator is further used in the adaptive weak Galerkin algorithm on the triangular, quadrilateral and other polygonal meshes. Numerical results are provided to demonstrate the effectiveness of the adaptive mesh refinement guided by this estimator.",

keywords = "A posteriori error estimator, Adaptive algorithm, Weak Galerkin finite element method, Weak gradient recovery",

author = "Ying Liu and Gang Wang and Mengyao Wu and Yufeng Nie",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2022",

month = may,

day = "1",

doi = "10.1016/j.cam.2021.113926",

language = "英语",

volume = "406",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - A recovery-based a posteriori error estimator of the weak Galerkin finite element method for elliptic problems

AU - Liu, Ying

AU - Wang, Gang

AU - Wu, Mengyao

AU - Nie, Yufeng

PY - 2022/5/1

Y1 - 2022/5/1

N2 - In this paper, we propose a recovery-type a posteriori error estimator of the weak Galerkin finite element method for the second order elliptic equation. The reliability and efficiency of the estimator are analyzed by a discrete H1-norm of the exact error. The estimator is further used in the adaptive weak Galerkin algorithm on the triangular, quadrilateral and other polygonal meshes. Numerical results are provided to demonstrate the effectiveness of the adaptive mesh refinement guided by this estimator.

AB - In this paper, we propose a recovery-type a posteriori error estimator of the weak Galerkin finite element method for the second order elliptic equation. The reliability and efficiency of the estimator are analyzed by a discrete H1-norm of the exact error. The estimator is further used in the adaptive weak Galerkin algorithm on the triangular, quadrilateral and other polygonal meshes. Numerical results are provided to demonstrate the effectiveness of the adaptive mesh refinement guided by this estimator.

KW - A posteriori error estimator

KW - Adaptive algorithm

KW - Weak Galerkin finite element method

KW - Weak gradient recovery

UR - http://www.scopus.com/inward/record.url?scp=85121116607&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2021.113926

DO - 10.1016/j.cam.2021.113926

M3 - 文章

AN - SCOPUS:85121116607

SN - 0377-0427

VL - 406

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

M1 - 113926

ER -

A recovery-based a posteriori error estimator of the weak Galerkin finite element method for elliptic problems

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this