Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion

Bangti Jin, Raytcho Lazarov, Joseph Pasciak, Zhi Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

78 Citations (Scopus)

Abstract

We consider the initial-boundary value problem for an inhomogeneous time-fractional diffusion equation with a homogeneous Dirichlet boundary condition, a vanishing initial data and a nonsmooth right-hand side in a bounded convex polyhedral domain. We analyse two semidiscrete schemes based on the standard Galerkin and lumped mass finite element methods. Almost optimal error estimates are obtained for right-hand side data f (x, t) ε L∞(0, T; Hq(ω)), ≤1≥ 1, for both semidiscrete schemes. For the lumped mass method, the optimal L2(ω)-norm error estimate requires symmetric meshes. Finally, twodimensional numerical experiments are presented to verify our theoretical results.
Original languageEnglish
Pages (from-to)561-582
Number of pages22
JournalIMA Journal of Numerical Analysis
Volume35
Issue number2
DOIs
Publication statusPublished - 15 Mar 2015
Externally publishedYes

Keywords

  • error estimate
  • inhomogeneous problem
  • lumped mass method
  • semidiscrete Galerkin scheme
  • time-fractional diffusion

ASJC Scopus subject areas

  • Mathematics(all)
  • Computational Mathematics
  • Applied Mathematics

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