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; Hq(ω)), ≤1≥ 1, for both semidiscrete schemes. For the lumped mass method, the optimal L2(ω)-norm error estimate requires symmetric meshes. Finally, twodimensional numerical experiments are presented to verify our theoretical results.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 561-582 |
| Number of pages | 22 |
| Journal | IMA Journal of Numerical Analysis |
| Volume | 35 |
| Issue number | 2 |
| DOIs | |
| State | Published - May 30 2014 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The research of B.J. was supported by NSF Grant DMS-1319052, that of R.L. and Z.Z. in part by US NSF Grant DMS-1016525 and that of J.P. by NSF Grant DMS-1216551. The work of all authors was also supported in part by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.