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dc.contributor.authorŞendur, Ali
dc.contributor.authorNeslitürk, Ali İhsan
dc.date.accessioned2017-02-09T13:02:57Z
dc.date.available2017-02-09T13:02:57Z
dc.date.issued2012-03
dc.identifier.citationŞendur, A., and Neslitürk, A. İ. (2012). Applications of the pseudo residual-free bubbles to the stabilization of convection-diffusion-reaction problems. Calcolo, 49(1), 1-19. doi:10.1007/s10092-011-0041-1en_US
dc.identifier.issn0008-0624
dc.identifier.urihttp://doi.org/10.1007/s10092-011-0041-1
dc.identifier.urihttp://hdl.handle.net/11147/4823
dc.description.abstractIt is known that the enrichment of the polynomial finite element space of degree 1 by bubble functions results in a stabilized scheme of the SUPG-type for the convection-diffusion-reaction problems. In particular, the residual-free bubbles (RFB) can assure stabilized methods, but they are usually difficult to compute, unless the configuration is simple. Therefore it is important to devise numerical algorithms that provide cheap approximations to the RFB functions, contributing a good stabilizing effect to the numerical method overall. Here we propose a stabilization technique based on the RFB method and particularly designed to treat the most interesting case of small diffusion. We replace the RFB functions by their cheap, yet efficient approximations which retain the same qualitative behavior. The approximate bubbles are computed on a suitable sub-grid, the choice of whose nodes are critical and determined by minimizing the residual of a local problem with respect to L 1 norm. The resulting numerical method has similar stability features with the RFB method for the whole range of problem parameters. This fact is also confirmed by numerical experiments. We also note that the location of the sub-grid nodes suggested by the strategy herein coincides with the one in Brezzi et al. (Math. Models Methods Appl. Sci. 13:445-461, 2003). © 2011 Springer-Verlag.en_US
dc.language.isoengen_US
dc.publisherSpringeren_US
dc.relation.isversionof10.1007/s10092-011-0041-1en_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectAugmented spaceen_US
dc.subjectResidual-free bubblesen_US
dc.subjectStabilized finite elementsen_US
dc.titleApplications of the pseudo residual-free bubbles to the stabilization of convection-diffusion-reaction problemsen_US
dc.typearticleen_US
dc.contributor.iztechauthorŞendur, Ali
dc.contributor.iztechauthorNeslitürk, Ali İhsan
dc.relation.journalCalcoloen_US
dc.contributor.departmentİYTE, Fen Fakültesi, Matematik Bölümüen_US
dc.identifier.volume49en_US
dc.identifier.issue1en_US
dc.identifier.startpage1en_US
dc.identifier.endpage19en_US
dc.identifier.wosWOS:000300577700001
dc.identifier.scopusSCOPUS:2-s2.0-84857446893


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