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Title: Residual-based a posteriori error estimation for hp-adaptive finite element methods for the Stokes equations

Abstract

We derive a residual-based a posteriori error estimator for the conforming hp-Adaptive Finite Element Method (hp-AFEM) for the steady state Stokes problem describing the slow motion of an incompressible fluid. This error estimator is obtained by extending the idea of a posteriori error estimation for the classical h-version of AFEM. We also establish the reliability and efficiency of the error estimator. The proofs are based on the well-known Clément-type interpolation operator introduced in [27] in the context of the hp-AFEM. Numerical experiments show the performance of an adaptive hp-FEM algorithm using the proposed a posteriori error estimator.

Authors:
 [1];  [2]; ORCiD logo [3]
  1. Texas A & M Univ., College Station, TX (United States)
  2. Colorado State Univ., Fort Collins, CO (United States)
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1649541
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Numerical Mathematics
Additional Journal Information:
Journal Volume: 27; Journal Issue: 4; Journal ID: ISSN 1570-2820
Publisher:
de Gruyter
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; adaptive finite element methods; hp finite element methods; error estimation; Stokes equations; 65N30; 65N15

Citation Formats

Ghesmati, Arezou, Bangerth, Wolfgang, and Turcksin, Bruno. Residual-based a posteriori error estimation for hp-adaptive finite element methods for the Stokes equations. United States: N. p., 2019. Web. https://doi.org/10.1515/jnma-2018-0047.
Ghesmati, Arezou, Bangerth, Wolfgang, & Turcksin, Bruno. Residual-based a posteriori error estimation for hp-adaptive finite element methods for the Stokes equations. United States. https://doi.org/10.1515/jnma-2018-0047
Ghesmati, Arezou, Bangerth, Wolfgang, and Turcksin, Bruno. Wed . "Residual-based a posteriori error estimation for hp-adaptive finite element methods for the Stokes equations". United States. https://doi.org/10.1515/jnma-2018-0047. https://www.osti.gov/servlets/purl/1649541.
@article{osti_1649541,
title = {Residual-based a posteriori error estimation for hp-adaptive finite element methods for the Stokes equations},
author = {Ghesmati, Arezou and Bangerth, Wolfgang and Turcksin, Bruno},
abstractNote = {We derive a residual-based a posteriori error estimator for the conforming hp-Adaptive Finite Element Method (hp-AFEM) for the steady state Stokes problem describing the slow motion of an incompressible fluid. This error estimator is obtained by extending the idea of a posteriori error estimation for the classical h-version of AFEM. We also establish the reliability and efficiency of the error estimator. The proofs are based on the well-known Clément-type interpolation operator introduced in [27] in the context of the hp-AFEM. Numerical experiments show the performance of an adaptive hp-FEM algorithm using the proposed a posteriori error estimator.},
doi = {10.1515/jnma-2018-0047},
journal = {Journal of Numerical Mathematics},
number = 4,
volume = 27,
place = {United States},
year = {2019},
month = {12}
}

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