eprintid: 1452455
rev_number: 41
eprint_status: archive
userid: 608
dir: disk0/01/45/24/55
datestamp: 2015-03-23 15:03:37
lastmod: 2020-02-13 07:39:11
status_changed: 2015-03-23 15:03:37
type: article
metadata_visibility: show
item_issues_count: 0
creators_name: Jin, B
creators_name: Lazarov, R
creators_name: Pasciak, J
creators_name: Zhou, Z
title: ERROR ANALYSIS OF A FINITE ELEMENT METHOD FOR THE SPACE-FRACTIONAL PARABOLIC EQUATION
ispublished: pub
divisions: UCL
divisions: A01
divisions: B04
divisions: C05
divisions: F48
keywords: finite element method, space fractional parabolic equation, semidiscrete scheme, fully discrete scheme, error estimate
note: Copyright © 2015, Society for Industrial and Applied Mathematics
abstract: We consider an initial boundary value problem for a one-dimensional fractional-order parabolic equation with a space fractional derivative of Riemann--Liouville type and order $\alpha\in (1,2)$. We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank--Nicolson method. Error estimates in the $L^2(D)$- and $H^{\alpha/2}(D)$-norm are derived for the semidiscrete scheme and in the $L^2(D)$-norm for the fully discrete schemes. These estimates cover both smooth and nonsmooth initial data and are expressed directly in terms of the smoothness of the initial data. Extensive numerical results are presented to illustrate the theoretical results.
date: 2014
official_url: http://dx.doi.org/10.1137/13093933X
vfaculties: VENG
oa_status: green
full_text_type: pub
primo: open
primo_central: open_green
verified: verified_manual
elements_source: WoS-Lite
elements_id: 987090
doi: 10.1137/13093933X
lyricists_name: Jin, Bangti
lyricists_id: BJINX59
full_text_status: public
publication: SIAM JOURNAL ON NUMERICAL ANALYSIS
volume: 52
number: 5
pagerange: 2272 - 2294
issn: 0036-1429
citation:        Jin, B;    Lazarov, R;    Pasciak, J;    Zhou, Z;      (2014)    ERROR ANALYSIS OF A FINITE ELEMENT METHOD FOR THE SPACE-FRACTIONAL PARABOLIC EQUATION.                   SIAM JOURNAL ON NUMERICAL ANALYSIS , 52  (5)   2272 - 2294.    10.1137/13093933X <https://doi.org/10.1137/13093933X>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/1452455/3/Jin._Pub.Version.pdf