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Title: A Fully Computable A Posteriori Error Estimate for the Stokes Equations on Polytopal Meshes

Abstract

Here in this paper, we present a simple a posteriori error estimate for the weak Galerkin finite element method for the Stokes equation. This residual type estimator can be applied to general meshes such as polytopal mesh or meshes with hanging nodes. The reliability and efficiency of the estimator are proved in this paper. Five numerical tests demonstrate the effectiveness and flexibility of the adaptive mesh refinement guided by the designed error estimator.

Authors:
 [1]; ORCiD logo [2];  [3]
  1. Florida State Univ., Tallahassee, FL (United States). Dept. of Mathematics
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
  3. Univ. of Tennessee, Chattanooga, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1531205
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
SIAM Journal on Numerical Analysis
Additional Journal Information:
Journal Volume: 57; Journal Issue: 1; Journal ID: ISSN 0036-1429
Publisher:
Society for Industrial and Applied Mathematics
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; weak Galerkin; finite element methods; Stokes equations; a posterior error estimate; polytopal meshes

Citation Formats

Bao, Feng, Mu, Lin, and Wang, Jin. A Fully Computable A Posteriori Error Estimate for the Stokes Equations on Polytopal Meshes. United States: N. p., 2019. Web. doi:10.1137/18M1171515.
Bao, Feng, Mu, Lin, & Wang, Jin. A Fully Computable A Posteriori Error Estimate for the Stokes Equations on Polytopal Meshes. United States. doi:10.1137/18M1171515.
Bao, Feng, Mu, Lin, and Wang, Jin. Tue . "A Fully Computable A Posteriori Error Estimate for the Stokes Equations on Polytopal Meshes". United States. doi:10.1137/18M1171515.
@article{osti_1531205,
title = {A Fully Computable A Posteriori Error Estimate for the Stokes Equations on Polytopal Meshes},
author = {Bao, Feng and Mu, Lin and Wang, Jin},
abstractNote = {Here in this paper, we present a simple a posteriori error estimate for the weak Galerkin finite element method for the Stokes equation. This residual type estimator can be applied to general meshes such as polytopal mesh or meshes with hanging nodes. The reliability and efficiency of the estimator are proved in this paper. Five numerical tests demonstrate the effectiveness and flexibility of the adaptive mesh refinement guided by the designed error estimator.},
doi = {10.1137/18M1171515},
journal = {SIAM Journal on Numerical Analysis},
number = 1,
volume = 57,
place = {United States},
year = {2019},
month = {1}
}

Journal Article:
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This content will become publicly available on January 1, 2020
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