Supraconvergence and Supercloseness of a Discretisation for Elliptic Third-kind Boundary-value Problems on Polygonal Domains
| dc.contributor.author | Emmrich, Etienne | |
| dc.date.accessioned | 2018-10-10T07:34:30Z | |
| dc.date.available | 2018-10-10T07:34:30Z | |
| dc.date.issued | 2007 | |
| dc.description.abstract | The 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.eissn | 1609-9389 | |
| dc.identifier.issn | 1609-4840 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/8310 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-7461 | |
| dc.language.iso | en | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject.ddc | 510 Mathematik | de |
| dc.subject.other | elliptic PDE | en |
| dc.subject.other | fully discrete FEM | en |
| dc.subject.other | nonuniform grid | en |
| dc.subject.other | supraconvergence | en |
| dc.subject.other | supercloseness of gradient | en |
| dc.title | Supraconvergence and Supercloseness of a Discretisation for Elliptic Third-kind Boundary-value Problems on Polygonal Domains | en |
| dc.type | Article | en |
| dc.type.version | publishedVersion | en |
| dcterms.bibliographicCitation.doi | 10.2478/cmam-2007-0008 | |
| dcterms.bibliographicCitation.issue | 2 | |
| dcterms.bibliographicCitation.journaltitle | Computational methods in applied mathematics | en |
| dcterms.bibliographicCitation.originalpublishername | De Gruyter | en |
| dcterms.bibliographicCitation.originalpublisherplace | Berlin | en |
| dcterms.bibliographicCitation.pageend | 162 | |
| dcterms.bibliographicCitation.pagestart | 135 | |
| dcterms.bibliographicCitation.volume | 7 | |
| tub.accessrights.dnb | free | |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | de |
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