Optimal error estimates for nonstationary singularly perturbed problems for low discretization orders

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dc.contributor.authorVlasák, Miloslav
dc.contributor.authorRoos, Hans–Göerg
dc.date.accessioned2017-11-02
dc.date.available2017-11-02
dc.date.issued2012
dc.description.abstractWe consider an unsteady 1D singularly perturbed convection–diffusion problem. We discretize such a problem by the linear finite element method (FEM) on a Shishkin mesh and by a discon- tinuous Galerkin method in time. We present optimal a priori error estimates for low order time discretizations.en
dc.formattextcs
dc.format.extent8 stran
dc.identifier.eissn1803-9790
dc.identifier.issn1803-9782
dc.identifier.otherACC_2012_4_17
dc.identifier.urihttps://dspace.tul.cz/handle/15240/21149
dc.language.isoen
dc.licenseCC BY-NC 4.0
dc.publisherTechnická univerzita v Liberci, Česká republikacs
dc.relation.isbasedonAHMED, N.; MATTHIES, G.; TOBISKA, L.; XIE, H.: Discontinuous Galerkin time step- ping with local projection stabilization for transient convection-diffusion-reaction prob- lems. Comput. Methods Appl. Mech. Eng., 200(21-22): pp. 1747-1756, 2011.
dc.relation.isbasedonCIARLET, P. G.: The finite element methods for elliptic problems. Repr., unabridged re- publ. of the orig. 1978. Classics in Applied Mathematics. 40. Philadelphia, PA: SIAM. xxiv, 530 p. , 2002.
dc.relation.isbasedonDOLEJŠÍ, V.; ROOS, H.-G.: BDF-FEM for parabolic singularly perturbed problems with exponential layers on layer-adapted meshes in space. Neural Parallel Sci. Comput., 18(2): pp. 221-235, 2010.
dc.relation.isbasedonFEISTAUER, M.; HÁ JEK, J.; ŠVADLENKA, K.: Space-time discontinuos Galerkin
dc.relation.isbasedonmethod for solving nonstationary convection-diffusion-reaction problems. Appl. Math., Praha, 52(3): pp. 197-233, 2007.
dc.relation.isbasedonKALAND, L.; ROOS, H.-G.: Parabolic singularly perturbed problems with exponential layers: robust discretizations using finite elements in space on Shishkin meshes. Int. J. Numer. Anal. Model., 7(3): pp. 593-606, 2010.
dc.relation.isbasedonROOS, H.-G.; STYNES, M.; TOBISKA, L.: Robust numerical methods for singularly perturbed differential equations. Convection-diffusion-reaction and flow problems. 2nd ed. Springer Series in Computational Mathematics 24. Berlin: Springer. xiv, 604 p., 2008. ISBN 978-3-540-34466-7/hbk.
dc.relation.isbasedonSCHO¨ TZAU, D.: hp-DGFEM for parabolic evolution problems. Application to diffusion and viscous incompressible flow. Ph.D. thesis, ETH Zu¨rich, 1999.
dc.relation.isbasedonTHOME´ E, V.: Galerkin finite element methods for parabolic problems. 2nd revised and expanded ed. Berlin: Springer. xii, 370 p., 2006. ISBN 3-540-33121-2/hbk.
dc.relation.ispartofACC Journalen
dc.relation.isrefereedtrue
dc.subjectConvection–diffusionen
dc.subjectShishkin meshen
dc.subjecttime discontinuous Galerkin methoden
dc.titleOptimal error estimates for nonstationary singularly perturbed problems for low discretization ordersen
dc.typeArticleen
local.accessopen
local.citation.epage154
local.citation.spage147
local.fulltextyesen
local.relation.issue4
local.relation.volume18
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