Error analysis of a finite element method for the space-fractional parabolic equation

Bangti Jin, Raytcho Lazarov, Joseph Pasciak, Zhi Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

70 Citations (Scopus)

Abstract

We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank-Nicolson method. Error estimates in the L2(D)- and Hα/2(D)-norm are derived for the semidiscrete scheme and in the L2(D)-norm for the fully discrete schemes. These estimates cover both smooth and nonsmooth initial data and are expressed directly in terms of the smoothness of the initial data. Extensive numerical results are presented to illustrate the theoretical results.
Original languageEnglish
Pages (from-to)2272-2294
Number of pages23
JournalSIAM Journal on Numerical Analysis
Volume52
Issue number5
DOIs
Publication statusPublished - 1 Jan 2014
Externally publishedYes

Keywords

  • Error estimate
  • Finite element method
  • Fully discrete scheme
  • Semidiscrete scheme
  • Space fractional parabolic equation

ASJC Scopus subject areas

  • Numerical Analysis

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