Asymptotically compatible schemes for space-time nonlocal diffusion equations

An Chen, Qiang Du, Changpin Li, Zhi Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

10 Citations (Scopus)

Abstract

Firstly, we show the uniqueness and existence of the weak solution of the nonlocal model, and study the local limit of the nonlocal model as horizon parameters approach zero. Particularly, it is shown that the convergence is uniform at a rate of O(δ+σ2), under certain regularity assumptions on initial and source data. Next we propose a fully discrete scheme, by exploiting the quadrature-based finite difference method in time and the Fourier spectral method in space, and show its stability. The numerical scheme is proved to be asymptotically compatible so that it preserves the local limiting behavior at the discrete level. Numerical experiments are provided to illustrate the theoretical results.
Original languageEnglish
Pages (from-to)361-371
Number of pages11
JournalChaos, Solitons and Fractals
Volume102
DOIs
Publication statusPublished - 1 Sep 2017
Externally publishedYes

Keywords

  • Asymptotically compatibility
  • Fourier spectral method
  • Local limit
  • Quadrature-based finite difference
  • Space-time nonlocal equation
  • Well-posedness

ASJC Scopus subject areas

  • Mathematics(all)

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