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Title: Weak Galerkin based a posteriori error estimates for second order elliptic interface problems on polygonal meshes

Abstract

In this paper, we present a posteriori error estimate of weak Galerkin (WG) finite element methods based on the second order elliptic interface problems. This estimate can be applied to polygonal meshes or meshes with hanging nodes. The reliability and efficiency of the designed error estimator has been proved in this work. Extensive numerical tests are performed to validate our algorithm. Finally, these results demonstrate the effectiveness of the adaptive mesh refinement guided by the proposed error estimator.

Authors:
ORCiD logo [1]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1531206
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 361; Journal Issue: C; Journal ID: ISSN 0377-0427
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
Weak Galerkin; Finite element methods; Second-order elliptic interface problems; A posterior error estimate; Polygonal meshes

Citation Formats

Mu, Lin. Weak Galerkin based a posteriori error estimates for second order elliptic interface problems on polygonal meshes. United States: N. p., 2019. Web. doi:10.1016/j.cam.2019.04.026.
Mu, Lin. Weak Galerkin based a posteriori error estimates for second order elliptic interface problems on polygonal meshes. United States. doi:10.1016/j.cam.2019.04.026.
Mu, Lin. Sat . "Weak Galerkin based a posteriori error estimates for second order elliptic interface problems on polygonal meshes". United States. doi:10.1016/j.cam.2019.04.026.
@article{osti_1531206,
title = {Weak Galerkin based a posteriori error estimates for second order elliptic interface problems on polygonal meshes},
author = {Mu, Lin},
abstractNote = {In this paper, we present a posteriori error estimate of weak Galerkin (WG) finite element methods based on the second order elliptic interface problems. This estimate can be applied to polygonal meshes or meshes with hanging nodes. The reliability and efficiency of the designed error estimator has been proved in this work. Extensive numerical tests are performed to validate our algorithm. Finally, these results demonstrate the effectiveness of the adaptive mesh refinement guided by the proposed error estimator.},
doi = {10.1016/j.cam.2019.04.026},
journal = {Journal of Computational and Applied Mathematics},
number = C,
volume = 361,
place = {United States},
year = {2019},
month = {5}
}

Journal Article:
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This content will become publicly available on May 11, 2020
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