eprintid: 1384737
rev_number: 29
eprint_status: archive
userid: 608
dir: disk0/01/38/47/37
datestamp: 2013-02-02 22:47:21
lastmod: 2021-09-25 23:07:16
status_changed: 2015-11-12 10:33:01
type: article
metadata_visibility: show
item_issues_count: 0
creators_name: Burman, E
title: A Unified Analysis for Conforming and Nonconforming Stabilized Finite Element Methods Using Interior Penalty
ispublished: pub
divisions: UCL
divisions: B04
divisions: C06
divisions: F59
keywords: convection diffusion problem, interior penalty, finite element approximation, Crouzeix-Raviart element
note: Copyright © 2005 Society for Industrial and Applied Mathematics
abstract: We discuss stabilized Galerkin approximations in a new framework, widening the scope from the usual dichotomy of the discontinuous Galerkin method on the one hand and Petrov--Galerkin methods such as the SUPG method on the other. The idea is to use interior penalty terms as a means of stabilizing the finite element method using conforming or nonconforming approximation, thus circumventing the need of a Petrov--Galerkin-type choice of spaces. This is made possible by adding a higher-order penalty term giving L2-control of the jumps in the gradients between adjacent elements. We consider convection-diffusion-reaction problems using piecewise linear approximations and prove optimal order a priori error estimates for two different finite element spaces, the standard H1-conforming space of piecewise linears and the nonconforming space of piecewise linear elements where the nodes are situated at the midpoint of the element sides (the Crouzeix--Raviart element). Moreover, we show how the formulation extends to discontinuous Galerkin interior penalty methods in a natural way by domain decomposition using Nitsche's method.
date: 2005-07-25
official_url: http://dx.doi.org/10.1137/S0036142903437374
vfaculties: VMPS
oa_status: green
full_text_type: pub
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_source: WoS-Lite
elements_id: 850170
doi: 10.1137/S0036142903437374
lyricists_name: Burman, Erik
lyricists_id: ENBUR31
full_text_status: public
publication: SIAM Journal on Numerical Analysis
volume: 43
number: 5
pagerange: 2012-2033
issn: 0036-1429
citation:        Burman, E;      (2005)    A Unified Analysis for Conforming and Nonconforming Stabilized Finite Element Methods Using Interior Penalty.                   SIAM Journal on Numerical Analysis , 43  (5)   pp. 2012-2033.    10.1137/S0036142903437374 <https://doi.org/10.1137/S0036142903437374>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/1384737/1/Burman_Sinum_IP_Bur.pdf