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Title: An a posteriori error estimator for the weak Galerkin least-squares finite-element method

Abstract

In this paper, we derive an a posteriori error estimator for the weak Galerkin least-squares (WG-LS) method applied to the reaction–diffusion equation. Here, we show that this estimator is both reliable and efficient, allowing it to be used for adaptive refinement. Due to the flexibility of the WG-LS discretization, we are able to design a simple and straightforward refinement scheme that is applicable to any shape regular polygonal mesh. Finally, we present numerical experiments that confirm the effectiveness of the estimator, and demonstrate the robustness and efficiency of the proposed adaptive WG-LS approach.

Authors:
 [1]; ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3]
  1. Tufts Univ., Medford, MA (United States). Dept. of Mathematics
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
  3. Univ. of Arkansas, Little Rock, AR (United States). Dept. of mathematics
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE; National Science Foundation (NSF)
OSTI Identifier:
1531207
Grant/Contract Number:  
AC05-00OR22725; DMS-1620016; DMS-1620063
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 362; Journal Issue: C; Journal ID: ISSN 0377-0427
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Weak Galerkin; Finite-element methods; Least-squares finite-element methods; Second-order elliptic problems

Citation Formats

Adler, James H., Hu, Xiaozhe, Mu, Lin, and Ye, Xiu. An a posteriori error estimator for the weak Galerkin least-squares finite-element method. United States: N. p., 2019. Web. doi:10.1016/j.cam.2018.09.049.
Adler, James H., Hu, Xiaozhe, Mu, Lin, & Ye, Xiu. An a posteriori error estimator for the weak Galerkin least-squares finite-element method. United States. doi:10.1016/j.cam.2018.09.049.
Adler, James H., Hu, Xiaozhe, Mu, Lin, and Ye, Xiu. Sun . "An a posteriori error estimator for the weak Galerkin least-squares finite-element method". United States. doi:10.1016/j.cam.2018.09.049.
@article{osti_1531207,
title = {An a posteriori error estimator for the weak Galerkin least-squares finite-element method},
author = {Adler, James H. and Hu, Xiaozhe and Mu, Lin and Ye, Xiu},
abstractNote = {In this paper, we derive an a posteriori error estimator for the weak Galerkin least-squares (WG-LS) method applied to the reaction–diffusion equation. Here, we show that this estimator is both reliable and efficient, allowing it to be used for adaptive refinement. Due to the flexibility of the WG-LS discretization, we are able to design a simple and straightforward refinement scheme that is applicable to any shape regular polygonal mesh. Finally, we present numerical experiments that confirm the effectiveness of the estimator, and demonstrate the robustness and efficiency of the proposed adaptive WG-LS approach.},
doi = {10.1016/j.cam.2018.09.049},
journal = {Journal of Computational and Applied Mathematics},
number = C,
volume = 362,
place = {United States},
year = {2019},
month = {12}
}

Journal Article:
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