Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion Academic Article uri icon

abstract

  • © 2014 Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. We consider the initial-boundary value problem for an inhomogeneous time-fractional diffusion equation with a homogeneous Dirichlet boundary condition, a vanishing initial data and a nonsmooth right-hand side in a bounded convex polyhedral domain. We analyse two semidiscrete schemes based on the standard Galerkin and lumped mass finite element methods. Almost optimal error estimates are obtained for right-hand side data f (x, t) ε L ∞ (0, T; H q (ω)), ≤1≥ 1, for both semidiscrete schemes. For the lumped mass method, the optimal L 2 (ω)-norm error estimate requires symmetric meshes. Finally, twodimensional numerical experiments are presented to verify our theoretical results.

author list (cited authors)

  • Jin, B., Lazarov, R., Pasciak, J., & Zhou, Z.

citation count

  • 77

publication date

  • May 2014