Mixed FEM for Time-Fractional Diffusion Problems with Time-Dependent Coefficients

Samir Karaa, Amiya K. Pani*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper, a mixed finite element method is applied in spatial directions while keeping time variable continuous to a class of time-fractional diffusion problems with time-dependent coefficients on a bounded convex polygonal domain. Based on an energy argument combined with a repeated application of an integral operator, optimal error estimates, which are optimal with respect to both approximation properties and regularity results, are derived for the semidiscrete problem with smooth as well as nonsmooth initial data. Specially, a priori error bounds for both primary and secondary variables in L2-norm are established. Since the comparison between Fortin projection and the mixed Galerkin approximation of the secondary variable yields an improved rate of convergence, therefore, as a by-product, we derive Lp-estimates for the error in primary variable. Finally, some numerical experiments are conducted to confirm our theoretical findings.

Original languageEnglish
Article number51
JournalJournal of Scientific Computing
Volume83
Issue number3
DOIs
Publication statusPublished - Jun 1 2020
Externally publishedYes

Keywords

  • Mixed finite element method
  • Optimal error estimates
  • Semidiscrete method
  • Smooth and nonsmooth initial data
  • Time-dependent coefficients
  • Time-fractional diffusion equation

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Cite this