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Numerical Analysis of a Second order Pure Lagrange–Galerkin Method for Convection-Diffusion Problems. Part I: Time Discretization
dc.contributor.author | Benítez, Marta | |
dc.contributor.author | Bermúdez, Alfredo | |
dc.date.accessioned | 2024-02-06T15:55:10Z | |
dc.date.available | 2024-02-06T15:55:10Z | |
dc.date.issued | 2012-04-17 | |
dc.identifier.citation | Benítez, M., & Bermúdez, A. (2012). Numerical Analysis of a Second Order Pure Lagrange–Galerkin Method for Convection-Diffusion Problems. Part I: Time Discretization. SIAM Journal on Numerical Analysis, 50(2), 858-882. https://doi.org/10.1137/100809982 | es_ES |
dc.identifier.issn | 0036-1429 | |
dc.identifier.issn | 1095-7170 (e-ISSN) | |
dc.identifier.uri | http://hdl.handle.net/2183/35444 | |
dc.description | This version of the article has been accepted for publication, after peer review, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1137/100809982 | es_ES |
dc.description.abstract | [Abstract]: We propose and analyze a second order pure Lagrangian method for variable coefficient convection-(possibly degenerate) diffusion equations with mixed Dirichlet-Robin boundary conditions. First, the method is rigorously introduced for exact and approximate characteristics. Next, l1(H1) stability is proved and l1(H1) error estimates of order O(Δt2) are obtained. Moreover, l1(L2) stability and l1(L2) error estimates of order O(Δt2) with constants bounded in the hyperbolic limit are shown. For the particular case of Dirichlet boundary conditions, diffusion tensor A = ϵI and right-hand side f = 0, the l1(H1) stability estimate is independent of ϵ. Moreover, for incompressible flows the constants in the stability inequalities are independent of the final time. In a second part of this work, the pure Lagrangian scheme will be combined with Galerkin discretization using finite elements spaces and numerical examples will be presented. | es_ES |
dc.description.sponsorship | This work was supported by Xunta de Galicia underresearch project INCITE09 207 047 PR and by Ministerio de Ciencia e Innovación (Spain) underresearch projects Consolider MATHEMATICA CSD2006-00032 and MTM2008-02483. Xunta de Galicia; INCITE09 207 047 PR | es_ES |
dc.language.iso | eng | es_ES |
dc.publisher | SIAM, Society for Industrial and Applied Mathematics | es_ES |
dc.relation | info:eu-repo/grantAgreement/MICINN/Plan Nacional de I+D+i 2008-2011/MTM2008-02483/ES/ANALISIS Y SIMULACION NUMERICA DE MODELOS MATEMATICOS CON APLICACIONES INDUSTRIALES | es_ES |
dc.relation | info:eu-repo/grantAgreement/MEC/Consolider-Ingenio/CSD2006-00032/ES/INGENIO-MATHEMATICA | es_ES |
dc.relation.uri | https://doi.org/10.1137/100809982 | es_ES |
dc.rights | This manuscript version is made available under the CC-BY 4.0 International license https://creativecommons.org/licenses/by/4.0/ | es_ES |
dc.subject | Convection-diffusion equation | es_ES |
dc.subject | Pure Lagrangian method | es_ES |
dc.subject | Characteristics method | es_ES |
dc.subject | Stability | es_ES |
dc.subject | Error estimates | es_ES |
dc.subject | Second order schemes | es_ES |
dc.title | Numerical Analysis of a Second order Pure Lagrange–Galerkin Method for Convection-Diffusion Problems. Part I: Time Discretization | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.rights.access | info:eu-repo/semantics/openAccess | es_ES |
UDC.journalTitle | SIAM Journal on Numerical Analysis | es_ES |
UDC.volume | 50 | es_ES |
UDC.issue | 2 | es_ES |
UDC.startPage | 858 | es_ES |
UDC.endPage | 882 | es_ES |
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