Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion

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 sta...

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Bibliographic Details
Published in:IMA journal of numerical analysis 2015-04, Vol.35 (2), p.561-582
Main Authors: Jin, B., Lazarov, R., Pasciak, J., Zhou, Z.
Format: Article
Language:English
Subjects:
Diffusion
Dirichlet problem
Errors
Finite element method
Galerkin methods
Mathematical analysis
Mathematical models
Optimization
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Summary: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 [Formula], - 1 < q less than or equal to 1, for both semidiscrete schemes. For the lumped mass method, the optimal L2( Omega )-norm error estimate requires symmetric meshes. Finally, two-dimensional numerical experiments are presented to verify our theoretical results.
ISSN:0272-4979
1464-3642
DOI:10.1093/imanum/dru018