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

abstract

• 2014 The Authors. 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.

authors

• Lazarov, Raytcho

published proceedings

• JOURNAL OF COMPUTATIONAL PHYSICS

altmetric score

• 0.25

author list (cited authors)

• Jin, B., Lazarov, R., Liu, Y., & Zhou, Z.

citation count

• 178

complete list of authors

• Jin, Bangti||Lazarov, Raytcho||Liu, Yikan||Zhou, Zhi

publication date

• January 2015

publisher

• Elsevier  Publisher

published in

• Journal of Computational Physics  Journal

keywords

• Caputo Derivative
• Error Estimate
• Finite Element Method
• Multi-term Time-fractional Diffusion Equation
• Semidiscrete Scheme

Digital Object Identifier (DOI)

• 10.1016/j.jcp.2014.10.051

start page

• 825

end page

• 843

volume

• 281

URL

• http://dx.doi.org/10.1016/j.jcp.2014.10.051