eprintid: 1384765
rev_number: 30
eprint_status: archive
userid: 608
dir: disk0/01/38/47/65
datestamp: 2013-02-02 22:54:06
lastmod: 2021-09-25 23:12:03
status_changed: 2016-03-22 15:35:51
type: article
metadata_visibility: show
item_issues_count: 0
creators_name: Burman, E
creators_name: Ern, A
title: Stabilized Galerkin approximation of convection-diffusion-reaction equations: Discrete maximum principle and convergence
ispublished: pub
divisions: UCL
divisions: B04
divisions: C06
divisions: F59
note: Copyright © 2005 American Mathematical Society. The copyright for this article reverts to public domain 28 years after publication.
abstract: We analyze a nonlinear shock-capturing scheme for H1-conform-ing, piecewise-affine finite element approximations of linear elliptic problems. The meshes are assumed to satisfy two standard conditions: a local quasi-uniformity property and the Xu-Zikatanov condition ensuring that the stiffness matrix associated with the Poisson equation is an M-matrix. A discrete maximum principle is rigorously established in any space dimension for convection-diffusion-reaction problems. We prove that the shock-capturing finite element solution converges to that without shock-capturing if the cell Péclet numbers are sufficiently small. Moreover, in the diffusion-dominated regime, the difference between the two finite element solutions super-converges with respect to the actual approximation error. Numerical experiments on test problems with stiff layers confirm the sharpness of the a priori error estimates.
date: 2005-06-07
official_url: http://dx.doi.org/10.1090/S0025-5718-05-01761-8
vfaculties: VMPS
oa_status: gold
full_text_type: pub
language: eng
primo: open
verified: verified_manual
elements_source: WoS-Lite
elements_id: 850201
doi: 10.1090/S0025-5718-05-01761-8
lyricists_name: Burman, Erik
lyricists_id: ENBUR31
full_text_status: restricted
publication: Mathematics of Computation
volume: 74
number: 252
pagerange: 1637-1652
issn: 0025-5718
citation:        Burman, E;    Ern, A;      (2005)    Stabilized Galerkin approximation of convection-diffusion-reaction equations: Discrete maximum principle and convergence.                   Mathematics of Computation , 74  (252)   pp. 1637-1652.    10.1090/S0025-5718-05-01761-8 <https://doi.org/10.1090/S0025-5718-05-01761-8>.       Gold open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/1384765/1/Burman_S0025-5718-05-01761-8.pdf