Galerkin FEM for Fractional Order Parabolic Equations with Initial Data in H − s , 0 ≤ s ≤ 1

Bangti Jin, Raytcho Lazarov, Joseph Pasciak, Zhi Zhou

Research output: Chapter in Book/Report/Conference proceedingChapter

11 Scopus citations

Abstract

We investigate semi-discrete numerical schemes based on the standard Galerkin and lumped mass Galerkin finite element methods for an initial-boundary value problem for homogeneous fractional diffusion problems with non-smooth initial data. We assume that Ω ⊂ ℝd , d = 1,2,3 is a convex polygonal (polyhedral) domain. We theoretically justify optimal order error estimates in L2- and H1-norms for initial data in H-s (Ω), 0 ≤ s ≤ 1. We confirm our theoretical findings with a number of numerical tests that include initial data v being a Dirac δ-function supported on a (d-1)-dimensional manifold. © 2013 Springer-Verlag.
Original languageEnglish (US)
Title of host publicationNumerical Analysis and Its Applications
PublisherSpringer Nature
Pages24-37
Number of pages14
ISBN (Print)9783642415142
DOIs
StatePublished - 2013
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The research of R. Lazarov and Z. Zhou was supportedin parts by US NSF Grant DMS-1016525 and J. Pasciak has been supported byNSF Grant DMS-1216551. The work of all authors has been supported also byAward No. KUS-C1-016-04, made by King Abdullah University of Science andTechnology (KAUST)
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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