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

9 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

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