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