dc.contributor.author | Gjerde, Ingeborg Gåseby | |
dc.contributor.author | Kumar, Kundan | |
dc.contributor.author | Nordbotten, Jan Martin | |
dc.date.accessioned | 2022-04-11T13:26:18Z | |
dc.date.available | 2022-04-11T13:26:18Z | |
dc.date.created | 2021-09-28T17:52:57Z | |
dc.date.issued | 2021 | |
dc.identifier.issn | 0036-1429 | |
dc.identifier.uri | https://hdl.handle.net/11250/2990972 | |
dc.description.abstract | In this work we consider the dual-mixed variational formulation of the Poisson equation with a line source. The analysis and approximation of this problem is nonstandard, as the line source causes the solutions to be singular. We start by showing that this problem admits a solution in appropriately weighted Sobolev spaces. Next, we show that given some assumptions on the problem parameters, the solution admits a splitting into higher- and lower-regularity terms. The lower-regularity terms are here explicitly known and capture the solution singularities. The higher-regularity terms, meanwhile, are defined as the solution of an associated mixed Poisson equation. With the solution splitting in hand, we then define a singularity removal--based mixed finite element method in which only the higher-regularity terms are approximated numerically. This method yields a significant improvement in the convergence rate when compared to approximating the full solution. In particular, we show that the singularity removal--based method yields optimal convergence rates for lowest-order Raviart--Thomas and discontinuous Lagrange elements. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | SIAM | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | A Mixed Approach to the Poisson Problem with Line Sources | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | publishedVersion | en_US |
dc.rights.holder | Copyright 2021 SIAM | en_US |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 2 | |
dc.identifier.doi | 10.1137/19M1296549 | |
dc.identifier.cristin | 1940071 | |
dc.source.journal | SIAM Journal on Numerical Analysis | en_US |
dc.source.pagenumber | 1117-1139 | en_US |
dc.relation.project | Norges forskningsråd: 250223 | en_US |
dc.identifier.citation | SIAM Journal on Numerical Analysis. 2021, 59 (2), 1117-1139. | en_US |
dc.source.volume | 59 | en_US |
dc.source.issue | 2 | en_US |