Finite volume element method for two-dimensional fractional subdiffusion problems

Samir Karaa*, Kassem Mustapha, Amiya K. Pani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)

Abstract

In this article, a semidiscrete spatial finite volume (FV) method is proposed and analyzed for approximating solutions of anomalous subdiffusion equations involving a temporal fractional derivative of order α ? (0, 1) in a two-dimensional convex domain. An optimal error estimate in the L∞ (L2)-norm is shown to hold. A superconvergence result is proved, and as a consequence, it is proved that a quasi-optimal order of convergence in the L∞ (L∞ )-norm holds. We also consider a fully discrete scheme that employs a FV method in space and a piecewise linear discontinuous Galerkin method to discretize in time. It is further shown that the convergence rate is of order h2 + k1+α, where h denotes the spatial discretization parameter and k represents the temporal discretization parameter. Numerical experiments indicate optimal convergence rates in both time and space, and also illustrate that the imposed regularity assumptions are pessimistic.

Original languageEnglish
Pages (from-to)945-964
Number of pages20
JournalIMA Journal of Numerical Analysis
Volume37
Issue number2
DOIs
Publication statusPublished - Apr 1 2017

Keywords

  • discontinuous Galerkin method
  • error analysis.
  • finite volume element
  • fractional diffusion

ASJC Scopus subject areas

  • Mathematics(all)
  • Computational Mathematics
  • Applied Mathematics

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