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The aggregated unfitted finite element method for elliptic problems
dc.contributor.author | Badia, Santiago |
dc.contributor.author | Verdugo Rojano, Francesc |
dc.contributor.author | Martín Huertas, Alberto Francisco |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental |
dc.date.accessioned | 2018-05-29T11:14:33Z |
dc.date.available | 2020-08-01T00:29:42Z |
dc.date.issued | 2018-07 |
dc.identifier.citation | Badia, S., Verdugo, F., Martín, A. F. The aggregated unfitted finite element method for elliptic problems. "Computer methods in applied mechanics and engineering", Juliol 2018, vol. 336, p. 533-553. |
dc.identifier.issn | 0045-7825 |
dc.identifier.other | https://arxiv.org/abs/1709.09122 |
dc.identifier.uri | http://hdl.handle.net/2117/117597 |
dc.description.abstract | Unfitted finite element techniques are valuable tools in different applications where the generation of body-fitted meshes is difficult. However, these techniques are prone to severe ill conditioning problems that obstruct the efficient use of iterative Krylov methods and, in consequence, hindersthe practical usage of unfitted methods for realistic large scale applications. In this work, we present a technique that addresses such conditioning problems by constructing enhanced finite element spaces based on a cell aggregation technique. The presented method, called aggregated unfitted finite element method, is easy to implement, and can be used, in contrast to previous works, in Galerkin approximations of coercive problems with conforming Lagrangian finite element spaces. The mathematical analysis of the method states that the condition number of the resulting linear system matrix scales as in standard finite elements for body-fitted meshes, without being affected by small cut cells, and that the method leads to the optimal finite element convergence order. These theoretical results are confirmed with 2D and 3D numerical experiments. |
dc.format.extent | 21 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits |
dc.subject.lcsh | Finite element method |
dc.subject.other | Unfitted finite elements Embedded boundary methods Ill-conditioning |
dc.title | The aggregated unfitted finite element method for elliptic problems |
dc.type | Article |
dc.subject.lemac | Elements finits, Mètode dels |
dc.contributor.group | Universitat Politècnica de Catalunya. ANiComp - Anàlisi numèrica i computació científica |
dc.identifier.doi | 10.1016/j.cma.2018.03.022 |
dc.description.peerreviewed | Peer Reviewed |
dc.relation.publisherversion | https://www.sciencedirect.com/science/article/pii/S0045782518301476 |
dc.rights.access | Open Access |
local.identifier.drac | 22745476 |
dc.description.version | Postprint (author's final draft) |
local.citation.author | Badia, S.; Verdugo, F.; Martín, A. F. |
local.citation.publicationName | Computer methods in applied mechanics and engineering |
local.citation.volume | 336 |
local.citation.startingPage | 533 |
local.citation.endingPage | 553 |
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