Duality estimates for the numerical solution of integral equations
type: Item
instance of: scholarly article
title: Duality estimates for the numerical solution of integral equations
zbMATH Open document ID: 0663.65141
DOI: 10.1007/BF01396766
author: Martin Costabel
author: Ernst P. Stephan
published in: Numerische Mathematik
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133322
review text: By a small modification of the statement and the proof of the Aubin- Nitsche lemma for Galerkin methods [cf. \textit{P. G. Ciarlet}, The finite element method for elliptic problems (1978; Zbl 0383.65058)] the authors arrive at duality estimates for the error of general projective methods. The estimates are applied to Galerkin methods as to boundary integral equations on plane domains with corners and and three-dimensional screen and crack problems, and to the collocation method as to the integral equation of the second kind with the double layer potential on a piecewise smooth curve. In the latter case, the integral equation is solved by nodal collocation using piecewise linear trial functions. In some cases the authors get higher order estimates where previous formulations of the duality arguments were not applicable. The estimates are confirmed by numerical results.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35C15
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 4084961
zbMATH Keywords: error estimates
zbMATH Keywords: Aubin-Nitsche lemma
zbMATH Keywords: Galerkin methods
zbMATH Keywords: projective methods
zbMATH Keywords: boundary integral equations
zbMATH Keywords: collocation method
zbMATH Keywords: double layer potential
zbMATH Keywords: numerical results
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4084961