A priori and a posteriori pseudostress-velocity mixed finite element error analysis for the stokes problem

Carsten Carstensen, Dongho Kim, Eun Jae Park

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

The pseudostress-velocity formulation of the stationary Stokes problem allows a Raviart-Thomas mixed finite element formulation with quasi-optimal convergence and some superconvergent reconstruction of the velocity. This local postprocessing gives rise to some averaging a posteriori error estimator with explicit constants for reliable error control. Standard residual-based explicit a posteriori error estimation is shown to be reliable and efficient and motivates adaptive mesh-refining algorithms. Numerical experiments confirm our theoretical findings and illustrate the accuracy of the guaranteed upper error bounds even with reduced regularity.

Original languageEnglish
Pages (from-to)2501-2523
Number of pages23
JournalSIAM Journal on Numerical Analysis
Volume49
Issue number6
DOIs
Publication statusPublished - 2011 Dec 1

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Stokes Problem
Mixed Finite Elements
Error Analysis
Error analysis
Reliable Control
A Posteriori Error Estimation
Adaptive Mesh
A Posteriori Error Estimators
Formulation
Error Control
Post-processing
Error Bounds
Averaging
Regularity
Numerical Experiment
Refining
Experiments
Standards

All Science Journal Classification (ASJC) codes

  • Numerical Analysis

Cite this

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A priori and a posteriori pseudostress-velocity mixed finite element error analysis for the stokes problem. / Carstensen, Carsten; Kim, Dongho; Park, Eun Jae.

In: SIAM Journal on Numerical Analysis, Vol. 49, No. 6, 01.12.2011, p. 2501-2523.

Research output: Contribution to journalArticle

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