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The tolerant qualocation method for variable-coefficient elliptic equations on curves

Sloan, IH; Tran, T

Description

The 'tolerant' modification of the qualocation method is studied for variable-coefficient elliptic equations on curves. The modification (in which the discrete innerproducts on the righthand side of the qualocation method are replaced by exact integration) allows the same high-order convergence as the standard spline qualocation method but with reduced smoothness assumptions on the exact solution. The study (improving upon previous work for constant-coefficient boundary integral equations)...[Show more]

dc.contributor.authorSloan, IH
dc.contributor.authorTran, T
dc.date.accessioned2015-12-10T23:11:20Z
dc.date.available2015-12-10T23:11:20Z
dc.identifier.issn0897-3962
dc.identifier.urihttp://hdl.handle.net/1885/63772
dc.description.abstractThe 'tolerant' modification of the qualocation method is studied for variable-coefficient elliptic equations on curves. The modification (in which the discrete innerproducts on the righthand side of the qualocation method are replaced by exact integration) allows the same high-order convergence as the standard spline qualocation method but with reduced smoothness assumptions on the exact solution. The study (improving upon previous work for constant-coefficient boundary integral equations) builds upon a recent extension of the standard qualocation method to equations with variable coefficients by Sloan and Wendland. In particular, it is shown that, with exactly the same 'qualocation' rules as in that recent work for the standard qualocation method, the tolerant version of the method achieves the full order of convergence of the standard method but with just the same smoothness assumption on the exact solution as in the Galerkin method. The tolerant version of the method therefore allows convergence of arbitrarily high order to be achieved (in appropriate negative norms, and for splines of high enough order) even when the exact solution is not smooth.
dc.publisherRocky Mountain Mathematics Consortium
dc.sourceJournal of Integral Equations and Applications
dc.titleThe tolerant qualocation method for variable-coefficient elliptic equations on curves
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume13
dc.date.issued2001
local.identifier.absfor010110 - Partial Differential Equations
local.identifier.ariespublicationMigratedxPub846
local.type.statusPublished Version
local.contributor.affiliationSloan, IH, University of New South Wales
local.contributor.affiliationTran, T, College of Physical and Mathematical Sciences, ANU
local.bibliographicCitation.startpage73
local.bibliographicCitation.lastpage98
local.identifier.doi10.1216/jiea/996986883
dc.date.updated2015-12-10T09:21:40Z
local.identifier.scopusID2-s2.0-84875311833
CollectionsANU Research Publications

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