Supraconvergence and Supercloseness of a Discretisation for Elliptic Third-kind Boundary-value Problems on Polygonal Domains

dc.contributor.authorEmmrich, Etienne
dc.date.accessioned2018-10-10T07:34:30Z
dc.date.available2018-10-10T07:34:30Z
dc.date.issued2007
dc.description.abstractThe third-kind boundary-value problem for a second-order elliptic equation on a polygonal domain with variable coefficients, mixed derivatives, and first-order terms is approximated by a linear finite element method with first-order accurate quadrature. The corresponding bilinear form does not need to be strongly positive. The discretisation is equivalent to a finite difference scheme. Although the discretisation is in general only first-order consistent, supraconvergence, i.e., convergence of higher order, is shown to take place even on nonuniform grids. If neither oblique boundary sections nor mixed derivatives occur, then the optimal order s is achieved. The supraconvergence result is equivalent to the supercloseness of the gradient.en
dc.identifier.eissn1609-9389
dc.identifier.issn1609-4840
dc.identifier.urihttps://depositonce.tu-berlin.de//handle/11303/8310
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-7461
dc.language.isoen
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject.ddc510 Mathematikde
dc.subject.otherelliptic PDEen
dc.subject.otherfully discrete FEMen
dc.subject.othernonuniform griden
dc.subject.othersupraconvergenceen
dc.subject.othersupercloseness of gradienten
dc.titleSupraconvergence and Supercloseness of a Discretisation for Elliptic Third-kind Boundary-value Problems on Polygonal Domainsen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.doi10.2478/cmam-2007-0008
dcterms.bibliographicCitation.issue2
dcterms.bibliographicCitation.journaltitleComputational methods in applied mathematicsen
dcterms.bibliographicCitation.originalpublishernameDe Gruyteren
dcterms.bibliographicCitation.originalpublisherplaceBerlinen
dcterms.bibliographicCitation.pageend162
dcterms.bibliographicCitation.pagestart135
dcterms.bibliographicCitation.volume7
tub.accessrights.dnbfree
tub.affiliationFak. 2 Mathematik und Naturwissenschaften>Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinde
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