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