eprintid: 1384711
rev_number: 29
eprint_status: archive
userid: 608
dir: disk0/01/38/47/11
datestamp: 2013-02-02 22:40:31
lastmod: 2021-11-23 01:14:12
status_changed: 2015-11-12 10:18:21
type: article
metadata_visibility: show
item_issues_count: 0
creators_name: Burman, E
creators_name: Zunino, P
title: A Domain Decomposition Method Based on Weighted Interior Penalties for Advection‐Diffusion‐Reaction Problems
ispublished: pub
divisions: UCL
divisions: B04
divisions: C06
divisions: F59
keywords: advection-diffusion problem, interior penalty, finite element approximation, domain decomposition, iterative methods, discontinuous coefficients
note: Copyright © 2006 Society for Industrial and Applied Mathematics
abstract: We propose a domain decomposition method for advection‐diffusion‐reaction equations based on Nitsche’s transmission conditions. The advection‐dominated case is stabilized using a continuous interior penalty approach based on the jumps in the gradient over element boundaries. We prove the convergence of the finite element solutions of the discrete problem to the exact solution and propose a parallelizable iterative method. The convergence of the resulting domain decomposition method is proved, and this result holds true uniformly with respect to the diffusion parameter. The numerical scheme that we propose here can thus be applied straightforwardly to diffusion‐dominated, advection‐dominated, and hyperbolic problems. Some numerical examples are presented in different flow regimes showing the influence of the stabilization parameter on the performance of the iterative method, and we compare our method with some other domain decomposition techniques for advection‐diffusion equations.
date: 2006-08-07
official_url: http://dx.doi.org/10.1137/050634736
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: 850147
doi: 10.1137/050634736
lyricists_name: Burman, Erik
lyricists_id: ENBUR31
full_text_status: public
publication: SIAM Journal on Numerical Analysis
volume: 44
number: 4
pagerange: 1612 - 1638
issn: 0036-1429
citation:        Burman, E;    Zunino, P;      (2006)    A Domain Decomposition Method Based on Weighted Interior Penalties for Advection‐Diffusion‐Reaction Problems.                   SIAM Journal on Numerical Analysis , 44  (4)   1612 - 1638.    10.1137/050634736 <https://doi.org/10.1137/050634736>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/1384711/1/Burman_BuZu_DD.pdf