Edge Residuals Dominate a Posteriori Error Estimates for Low Order Finite Element Methods

Edge Residuals Dominate a Posteriori Error Estimates for Low Order Finite Element Methods

We prove that, up to higher order perturbation terms, edge residuals yield global upper and local lower bounds on the error of linear finite element methods both in H1- and L2-norms. We present two proofs: one uses the standard L2-projection and the other relies on a new, weighted Clement-type inter...

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Veröffentlicht in:SIAM journal on numerical analysis 1999, Vol.36 (5), p.1571-1587
Hauptverfasser: Carstensen, Carsten, Verfurth, Rudiger
Format: Artikel
Sprache:eng
Schlagworte:
A posteriori knowledge
Boundary conditions
Error rates
Estimation methods
Estimators
Exact sciences and technology
Finite element method
Integral equations, integral transforms
Interpolation
Mathematical functions
Mathematics
Norms
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Partial differential equations, boundary value problems
Sciences and techniques of general use
Triangulation
Vertices
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Zusammenfassung:We prove that, up to higher order perturbation terms, edge residuals yield global upper and local lower bounds on the error of linear finite element methods both in H1- and L2-norms. We present two proofs: one uses the standard L2-projection and the other relies on a new, weighted Clement-type interpolation operator.
ISSN:0036-1429
1095-7170
DOI:10.1137/S003614299732334X