A Posteriori Error Estimators for Nonconforming Approximation of Some Quasi-Newtonian Flows

This paper deals with a posteriori error estimators for nonconforming approximations of quasi-Newtonian flows. We consider the Crouzeix-Raviart piecewise linear approximations of scalar elliptic problems and define an error estimator. When Ω is a simply connected domain, the error is dominated by th...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 1997-08, Vol.34 (4), p.1600-1615
Main Author: Padra, Claudio
Format: Article
Language:English
Subjects:
A posteriori knowledge
Analytical estimating
Approximation
Curl
Error analysis
Error rates
Estimation methods
Estimators
Exact sciences and technology
Finite element method
Inequality
Interpolation
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, boundary value problems
Sciences and techniques of general use
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Summary:This paper deals with a posteriori error estimators for nonconforming approximations of quasi-Newtonian flows. We consider the Crouzeix-Raviart piecewise linear approximations of scalar elliptic problems and define an error estimator. When Ω is a simply connected domain, the error is dominated by the estimator. This estimator can be generalized to higher-order elements. We define a posteriori error estimators for the Fortin-Soulie piecewise quadratic approximations of quasi-Newtonian flows and prove that the error is dominated by the estimator. This estimator can be computed locally in terms of the approximate solution and is therefore suitable for adaptive refinement.
ISSN:0036-1429
1095-7170
DOI:10.1137/S0036142994278322