Publication: An efficient numerical method for singularly perturbed time dependent parabolic 2D convection-diffusion systems
| dc.contributor.author | Clavero, Carmelo | |
| dc.contributor.author | Jorge Ulecia, Juan Carlos | |
| dc.contributor.department | Ingeniería Matemática e Informática | es_ES |
| dc.contributor.department | Matematika eta Informatika Ingeniaritza | eu |
| dc.contributor.department | Institute of Smart Cities - ISC | en |
| dc.date.accessioned | 2019-08-09T07:27:39Z | |
| dc.date.available | 2021-07-01T23:00:14Z | |
| dc.date.issued | 2018 | |
| dc.description.abstract | In this paper we deal with solving efficiently 2D linear parabolic singularly perturbed systems of convection–diffusion type. We analyze only the case of a system of two equations where both of them feature the same diffusion parameter. Nevertheless, the method is easily extended to systems with an arbitrary number of equations which have the same diffusion coefficient. The fully discrete numerical method combines the upwind finite difference scheme, to discretize in space, and the fractional implicit Euler method, together with a splitting by directions and components of the reaction–convection–diffusion operator, to discretize in time. Then, if the spatial discretization is defined on an appropriate piecewise uniform Shishkin type mesh, the method is uniformly convergent and it is first order in time and almost first order in space. The use of a fractional step method in combination with the splitting technique to discretize in time, means that only tridiagonal linear systems must be solved at each time level of the discretization. Moreover, we study the order reduction phenomenon associated with the time dependent boundary conditions and we provide a simple way of avoiding it. Some numerical results, which corroborate the theoretical established properties of the method, are shown. | en |
| dc.description.sponsorship | This research was partially supported by the project MTM2014-52859-P and by the Aragón Government and European Social Fund, Spain (group E24–17R ). | en |
| dc.embargo.lift | 2021-07-01 | |
| dc.embargo.terms | 2021-07-01 | |
| dc.format.extent | 23 p. | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.doi | 10.1016/j.cam.2018.10.033 | |
| dc.identifier.issn | 0377-0427 | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/34215 | |
| dc.language.iso | eng | en |
| dc.publisher | Elsevier | en |
| dc.relation.ispartof | Journal of Computational and Applied Mathematics | en |
| dc.relation.projectID | info:eu-repo/grantAgreement/MINECO//MTM2014-52859-P/ES/ | en |
| dc.relation.publisherversion | https://doi.org/10.1016/j.cam.2018.10.033 | |
| dc.rights | © 2018 Elsevier B.V. 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 | Fractional implicit Euler | en |
| dc.subject | Order reduction | en |
| dc.subject | Parabolic systems | en |
| dc.subject | Shishkin meshes | en |
| dc.subject | Splitting by components | en |
| dc.subject | Uniform convergence | en |
| dc.title | An efficient numerical method for singularly perturbed time dependent parabolic 2D convection-diffusion systems | 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 | |
| relation.isAuthorOfPublication | 057cf9b6-54a9-4331-ade0-71ca16d5b57b | |
| relation.isAuthorOfPublication.latestForDiscovery | 057cf9b6-54a9-4331-ade0-71ca16d5b57b |