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A Remark on Parabolic Smoothing and the Finite Element Method

1980; Society for Industrial and Applied Mathematics; Volume: 17; Issue: 1 Linguagem: Inglês

10.1137/0717005

1095-7170

Lars B. Wahlbin,

Electromagnetic Simulation and Numerical Methods

Previous article Next article A Remark on Parabolic Smoothing and the Finite Element MethodLars B. WahlbinLars B. Wahlbinhttps://doi.org/10.1137/0717005PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract The extent to which the finite element method takes advantage of the smoothing property in parabolic problems is discussed. In particular, the effect of numerical integration is considered.[1] Garth A. Baker, , James H. Bramble and , Vidar Thomée, Single step Galerkin approximations for parabolic problems, Math. Comp., 31 (1977), 818–847 56:7252 0378.65061 CrossrefISIGoogle Scholar[2] J. H. Bramble and , S. Hilbert, Bounds for a class of linear functionals with applications to Hermite interpolation, Numer. Math., 16 (1970/1971), 362–369 44:7704 0214.41405 CrossrefISIGoogle Scholar[3] J. H. Bramble, , A. H. Schatz, , V. Thomée and , L. B. 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Numér., 12 (1978), 173–202, v 58:19236 0932.65103 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails High-order ADI finite difference schemes for parabolic equations in the combination technique with application in financeJournal of Computational and Applied Mathematics, Vol. 316 | 1 May 2017 Cross Ref Smoothing schemes for reaction-diffusion systems with nonsmooth dataJournal of Computational and Applied Mathematics, Vol. 223, No. 1 | 1 Jan 2009 Cross Ref Smoothing with positivity-preserving Padé schemes for parabolic problems with nonsmooth dataNumerical Methods for Partial Differential Equations, Vol. 21, No. 3 | 29 September 2004 Cross Ref Local behavior in finite element methodsFinite Element Methods (Part 1) | 1 Jan 1991 Cross Ref The Finite Element Method for Parabolic ProblemsMathematical Theory of Finite and Boundary Element Methods | 1 Jan 1990 Cross Ref Error estimates for spatially discrete approximations of semilinear parabolic equations with nonsmooth initial dataMathematics of Computation, Vol. 49, No. 180 | 1 January 1987 Cross Ref On the Smoothing Property of the Galerkin Method for Parabolic EquationsMitchell Luskin and Rolf RannacherSIAM Journal on Numerical Analysis, Vol. 19, No. 1 | 17 July 2006AbstractPDF (1252 KB)Fast Numerical Solution of Time-Periodic Parabolic Problems by a Multigrid MethodWolfgang HackbuschSIAM Journal on Scientific and Statistical Computing, Vol. 2, No. 2 | 16 May 2012AbstractPDF (781 KB) Volume 17, Issue 1| 1980SIAM Journal on Numerical Analysis History Submitted:26 January 1979Published online:17 July 2006 InformationCopyright © 1980 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0717005Article page range:pp. 33-38ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics