Publication: Decoupling mixed finite elements on hierarchical triangular grids for parabolic problems
dc.contributor.author | Arrarás Ventura, Andrés | |
dc.contributor.author | Portero Egea, Laura | |
dc.contributor.department | Ingeniería Matemática e Informática | es_ES |
dc.contributor.department | Matematika eta Informatika Ingeniaritza | eu |
dc.date.accessioned | 2020-11-11T10:24:57Z | |
dc.date.available | 2020-11-11T10:24:57Z | |
dc.date.issued | 2018 | |
dc.description.abstract | In this paper, we propose a numerical method for the solution of time-dependent flow problems in mixed form. Such problems can be efficiently approximated on hierarchical grids, obtained from an unstructured coarse triangulation by using a regular refinement process inside each of the initial coarse elements. If these elements are considered as subdomains, we can formulate a non-overlapping domain decomposition method based on the lowest-order Raviart–Thomas elements, properly enhanced with Lagrange multipliers on the boundaries of each subdomain (excluding the Dirichlet edges). A suitable choice of mixed finite element spaces and quadrature rules yields a cell-centered scheme for the pressures with a local 10-point stencil. The resulting system of differential-algebraic equations is integrated in time by the Crank–Nicolson method, which is known to be a stiffly accurate scheme. As a result, we obtain independent subdomain linear systems that can be solved in parallel. The behavior of the algorithm is illustrated on a variety of numerical experiments. | en |
dc.description.sponsorship | This work was partially supported by MINECO grant MTM2014-52859. | en |
dc.format.extent | 35 p. | |
dc.format.mimetype | application/pdf | en |
dc.identifier.doi | 10.1016/j.amc.2017.07.042 | |
dc.identifier.issn | 0096-3003 | |
dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/38632 | |
dc.language.iso | eng | en |
dc.publisher | Elsevier | en |
dc.relation.ispartof | Applied Mathematics and Computation, 2018, 319, 662-680 | en |
dc.relation.projectID | info:eu-repo/grantAgreement/MINECO//MTM2014-52859-P/ES/ | en |
dc.relation.publisherversion | https://doi.org/10.1016/j.amc.2017.07.042 | |
dc.rights | © 2017 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0 | en |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | en |
dc.rights.accessRights | Acceso abierto / Sarbide irekia | es |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
dc.subject | Cell-centered finite difference | en |
dc.subject | Domain decomposition | en |
dc.subject | Hierarchical grid | en |
dc.subject | Lagrange multiplier | en |
dc.subject | Mixed finite element | en |
dc.subject | Parabolic problem | en |
dc.title | Decoupling mixed finite elements on hierarchical triangular grids for parabolic problems | en |
dc.type | info:eu-repo/semantics/article | |
dc.type.version | info:eu-repo/semantics/acceptedVersion | en |
dc.type.version | Versión aceptada / Onetsi den bertsioa | es |
dspace.entity.type | Publication | |
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relation.isAuthorOfPublication | 880f9145-4259-4d01-95ec-5fc15ea7c71a | |
relation.isAuthorOfPublication.latestForDiscovery | 92e469b3-1f37-40ea-b002-628bb00fbc74 |