dc.contributor.author | Huynh, Dinh Bao Phuong | |
dc.contributor.author | Knezevic, David | |
dc.contributor.author | Chen, Y. | |
dc.contributor.author | Hesthaven, J. S. | |
dc.contributor.author | Patera, Anthony T. | |
dc.date.accessioned | 2011-06-17T15:19:13Z | |
dc.date.available | 2011-06-17T15:19:13Z | |
dc.date.issued | 2010-06 | |
dc.date.submitted | 2009-12 | |
dc.identifier.issn | 0045-7825 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/64476 | |
dc.description.abstract | We present a new approach for the construction of lower bounds for the inf-sup stability constants required in a posteriori error analysis of reduced basis approximations to affinely parametrized partial differential equations. We combine the “linearized” inf-sup statement of the natural-norm approach with the approximation procedure of the Successive Constraint Method (SCM): the former (natural-norm) provides an economical parameter expansion and local concavity in parameter—a small(er) optimization problem which enjoys intrinsic lower bound properties; the latter (SCM) provides a systematic optimization framework—a Linear Program (LP) relaxation which readily incorporates continuity and stability constraints. The natural-norm SCM requires a parameter domain decomposition: we propose a greedy algorithm for selection of the SCM control points as well as adaptive construction of the optimal subdomains. The efficacy of the natural-norm SCM is illustrated through numerical results for two types of non-coercive problems: the Helmholtz equation (for acoustics, elasticity, and electromagnetics), and the convection–diffusion equation. | en_US |
dc.description.sponsorship | United States. Air Force Office of Scientific Research (Grant No. FA 9550-07-1-0425) | en_US |
dc.language.iso | en_US | |
dc.publisher | Elsevier ScienceDirect | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1016/j.cma.2010.02.011 | en_US |
dc.rights | Creative Commons Attribution-Noncommercial-Share Alike 3.0 | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/3.0/ | en_US |
dc.source | MIT web domain | en_US |
dc.title | A natural-norm Successive Constraint Method for inf-sup lower bounds | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Huynh, D.B.P. et al. “A natural-norm Successive Constraint Method for inf-sup lower bounds.” Computer Methods in Applied Mechanics and Engineering 199.29-32 (2010) : 1963-1975.Copyright © 2010, Elsevier | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mechanical Engineering | en_US |
dc.contributor.approver | Patera, Anthony T. | |
dc.contributor.mitauthor | Knezevic, David | |
dc.contributor.mitauthor | Patera, Anthony T. | |
dc.relation.journal | Computer Methods in Applied Mechanics and Engineering | en_US |
dc.eprint.version | Author's final manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dspace.orderedauthors | Huynh, D.B.P.; Knezevic, D.J.; Chen, Y.; Hesthaven, J.S.; Patera, A.T. | en |
dc.identifier.orcid | https://orcid.org/0000-0002-2631-6463 | |
mit.license | OPEN_ACCESS_POLICY | en_US |
mit.metadata.status | Complete | |