Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion
KAUST Grant NumberKUS-C1-016-04
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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.
CitationJin B, Lazarov R, Pasciak J, Zhou Z (2014) Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion. IMA Journal of Numerical Analysis 35: 561–582. Available: http://dx.doi.org/10.1093/imanum/dru018.
SponsorsThe 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).
PublisherOxford University Press (OUP)