Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/78610
Title: Space-time Petrov-Galerkin FEM for fractional diffusion problems
Authors: Duan, BP
Jin, BT
Lazarov, R
Pasciak, J
Zhou, Z 
Keywords: Space-Time Finite Element Method
Petrov-Galerkin Method
Fractional Diffusion
Error Estimates
Issue Date: 2018
Publisher: Walter de Gruyter GmbH
Source: Computational methods in applied mathematics, Jan. 2018, v. 18, no. 1, p. 1-20 How to cite?
Journal: Computational methods in applied mathematics 
Abstract: We present and analyze a space-time Petrov-Galerkin finite element method for a time-fractional diffusion equation involving a Riemann-Liouville fractional derivative of order alpha is an element of(0, 1) in time and zero initial data. We derive a proper weak formulation involving different solution and test spaces and show the inf-sup condition for the bilinear form and thus itswell-posedness. Further, we develop a novel finite element formulation, show the well-posedness of the discrete problem, and derive error bounds in both energy and L-2 norms for the finite element solution. In the proof of the discrete inf-sup condition, a certain nonstandard L-2 stability property of the L-2 projection operator plays a key role. We provide extensive numerical examples to verify the convergence analysis.
URI: http://hdl.handle.net/10397/78610
ISSN: 1609-4840
EISSN: 1609-9389
DOI: 10.1515/cmam-2017-0026
Appears in Collections:Journal/Magazine Article

Access
View full-text via PolyU eLinks SFX Query
Show full item record

SCOPUSTM   
Citations

4
Citations as of Apr 3, 2019

WEB OF SCIENCETM
Citations

3
Last Week
0
Last month
Citations as of Apr 6, 2019

Page view(s)

34
Citations as of May 21, 2019

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.