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 / Conference proceedingConference article published in proceeding or bookAcademic researchpeer-review

9 Citations (Scopus)

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.
Original languageEnglish
Title of host publicationNumerical Analysis and Its Applications - 5th International Conference, NAA 2012, Revised Selected Papers
Pages24-37
Number of pages14
DOIs
Publication statusPublished - 7 Nov 2013
Externally publishedYes
Event5th International Conference on Numerical Analysis and Applications, NAA 2012 - Lozenetz, Bulgaria
Duration: 15 Jun 201320 Jun 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8236 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference5th International Conference on Numerical Analysis and Applications, NAA 2012
Country/TerritoryBulgaria
CityLozenetz
Period15/06/1320/06/13

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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