The Galerkin finite element method for a multi-term time-fractional diffusion equation

Bangti Jin, Raytcho Lazarov, Yikan Liu, Zhi Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

233 Citations (Scopus)


We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite element method using continuous piecewise linear functions. Nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived, which cover both smooth and nonsmooth data. Further we develop a fully discrete scheme based on a finite difference discretization of the time-fractional derivatives, and discuss its stability and error estimate. Extensive numerical experiments for one- and two-dimensional problems confirm the theoretical convergence rates.
Original languageEnglish
Pages (from-to)825-843
Number of pages19
JournalJournal of Computational Physics
Publication statusPublished - 5 Jan 2015
Externally publishedYes


  • Caputo derivative
  • Error estimate
  • Finite element method
  • Multi-term time-fractional diffusion equation
  • Semidiscrete scheme

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications


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