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

Ghesmati, Arezou; Bangerth, Wolfgang; Turcksin, Bruno

doi:10.1515/jnma-2018-0047

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

Journal Article · Tue Dec 17 23:00:00 EST 2019 · Journal of Numerical Mathematics

DOI:https://doi.org/10.1515/jnma-2018-0047· OSTI ID:1649541

Ghesmati, Arezou ^[1]; Bangerth, Wolfgang ^[2]; ^[3]

Texas A & M Univ., College Station, TX (United States)
Colorado State Univ., Fort Collins, CO (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1649541

Journal Information:: Journal of Numerical Mathematics, Journal Name: Journal of Numerical Mathematics Journal Issue: 4 Vol. 27; ISSN 1570-2820

Publisher:: de GruyterCopyright Statement

Country of Publication:: United States

Language:: English

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65N15
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97 MATHEMATICS AND COMPUTING
Stokes equations
adaptive finite element methods
error estimation
hp finite element methods

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

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