Two fully discrete schemes for fractional diffusion and diffusion-wave equations with nonsmooth data

Bangti Jin, Raytcho Lazarov, Zhi Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

149 Citations (Scopus)

Abstract

We consider initial/boundary value problems for the subdiffusion and diffusion-wave equations involving a Caputo fractional derivative in time. We develop two fully discrete schemes based on the piecewise linear Galerkin finite element method in space and convolution quadrature in time with the generating function given by the backward Euler method/second-order backward difference method, and establish error estimates optimal with respect to the regularity of problem data. These two schemes are first- and second-order accurate in time for both smooth and nonsmooth data. Extensive numerical experiments for two-dimensional problems confirm the convergence analysis and robustness of the schemes with respect to data regularity.
Original languageEnglish
Pages (from-to)A146-A170
JournalSIAM Journal on Scientific Computing
Volume38
Issue number1
DOIs
Publication statusPublished - 1 Jan 2016
Externally publishedYes

Keywords

  • Convolution quadrature
  • Diffusion wave
  • Error estimate
  • Finite element method
  • Fractional diffusion

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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