The Galerkin Finite Element Method for A Multi-term Time-Fractional Diffusion equation

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. Nearl...

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Bibliographic Details
Published in:arXiv.org
Main Authors: Jin, Bangti, Lazarov, Raytcho, Liu, Yikan, Zhou, Zhi
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 31.01.2014
Subjects:
Boundary value problems
Continuity (mathematics)
Derivatives
Finite difference method
Finite element analysis
Finite element method
Galerkin method
Linear functions
Mathematical analysis
Nonlinear programming
ISSN:2331-8422
Online Access:Get full text
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Summary: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-dimension problems confirm the convergence rates of the theoretical results.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
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ISSN:2331-8422
DOI:10.48550/arxiv.1401.8049