Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations: Application to Transport and Continuum Mechanics
In this paper we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for linear functional outputs of affinely parametrized elliptic coercive partial differential equations. The essential ingredients are (primal-dual) Galerkin projection onto a low-dimensi...
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| Veröffentlicht in: | Archives of computational methods in engineering 2008-09, Vol.15 (3), p.229-275 |
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| creator | Rozza, G. Huynh, D. B. P. Patera, A. T. |
| description | In this paper we consider (hierarchical, Lagrange) reduced basis approximation and
a posteriori
error estimation for linear functional outputs of affinely parametrized elliptic coercive partial differential equations. The essential ingredients are (primal-dual) Galerkin projection onto a low-dimensional space associated with a smooth “parametric manifold”—dimension reduction; efficient and effective greedy sampling methods for identification of optimal and numerically stable approximations—rapid convergence;
a posteriori
error estimation procedures—rigorous and sharp bounds for the linear-functional outputs of interest; and Offline-Online computational decomposition strategies—minimum
marginal cost
for high performance in the real-time/embedded (e.g., parameter-estimation, control) and many-query (e.g., design optimization, multi-model/scale) contexts. We present illustrative results for heat conduction and convection-diffusion, inviscid flow, and linear elasticity; outputs include transport rates, added mass, and stress intensity factors. |
| doi_str_mv | 10.1007/s11831-008-9019-9 |
| format | Article |
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a posteriori
error estimation for linear functional outputs of affinely parametrized elliptic coercive partial differential equations. The essential ingredients are (primal-dual) Galerkin projection onto a low-dimensional space associated with a smooth “parametric manifold”—dimension reduction; efficient and effective greedy sampling methods for identification of optimal and numerically stable approximations—rapid convergence;
a posteriori
error estimation procedures—rigorous and sharp bounds for the linear-functional outputs of interest; and Offline-Online computational decomposition strategies—minimum
marginal cost
for high performance in the real-time/embedded (e.g., parameter-estimation, control) and many-query (e.g., design optimization, multi-model/scale) contexts. We present illustrative results for heat conduction and convection-diffusion, inviscid flow, and linear elasticity; outputs include transport rates, added mass, and stress intensity factors.</description><identifier>ISSN: 1134-3060</identifier><identifier>EISSN: 1886-1784</identifier><identifier>DOI: 10.1007/s11831-008-9019-9</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Approximation ; Design optimization ; Engineering ; Engineering Sciences ; Mathematical and Computational Engineering ; Mechanics ; Original Paper ; Partial differential equations ; Structural mechanics ; Studies</subject><ispartof>Archives of computational methods in engineering, 2008-09, Vol.15 (3), p.229-275</ispartof><rights>CIMNE, Barcelona, Spain 2008</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c2179-eb7a43b7305944f34faef6aa7454eabf21ad1f1310fb101c0fb0d9cd28ae91e83</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11831-008-9019-9$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11831-008-9019-9$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>230,314,780,784,885,27924,27925,41488,42557,51319</link.rule.ids><backlink>$$Uhttps://hal.science/hal-01722593$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Rozza, G.</creatorcontrib><creatorcontrib>Huynh, D. B. P.</creatorcontrib><creatorcontrib>Patera, A. T.</creatorcontrib><title>Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations: Application to Transport and Continuum Mechanics</title><title>Archives of computational methods in engineering</title><addtitle>Arch Computat Methods Eng</addtitle><description>In this paper we consider (hierarchical, Lagrange) reduced basis approximation and
a posteriori
error estimation for linear functional outputs of affinely parametrized elliptic coercive partial differential equations. The essential ingredients are (primal-dual) Galerkin projection onto a low-dimensional space associated with a smooth “parametric manifold”—dimension reduction; efficient and effective greedy sampling methods for identification of optimal and numerically stable approximations—rapid convergence;
a posteriori
error estimation procedures—rigorous and sharp bounds for the linear-functional outputs of interest; and Offline-Online computational decomposition strategies—minimum
marginal cost
for high performance in the real-time/embedded (e.g., parameter-estimation, control) and many-query (e.g., design optimization, multi-model/scale) contexts. We present illustrative results for heat conduction and convection-diffusion, inviscid flow, and linear elasticity; outputs include transport rates, added mass, and stress intensity factors.</description><subject>Approximation</subject><subject>Design optimization</subject><subject>Engineering</subject><subject>Engineering Sciences</subject><subject>Mathematical and Computational Engineering</subject><subject>Mechanics</subject><subject>Original Paper</subject><subject>Partial differential equations</subject><subject>Structural mechanics</subject><subject>Studies</subject><issn>1134-3060</issn><issn>1886-1784</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp1kcFOGzEQhldVkZpCH6A3S5w4LPXY3uz6GNKlqRSpEWrP1mR3DEbLOrE3EfAEfWycbEG9cBqP_f2_PPNn2Vfgl8B5-S0CVBJyzqtcc9C5_pBNoKqmOZSV-pjOIFUu-ZR_yj7HeM95obQWk-zvDbW7hlp2hdFFNttsgn90Dzg43zPsW4Zs5eNAwfngWB2CD6yOwythUzuz1vXUPbEVBnygIbjn5Fd3ndsMrmFzT6Fxezo8Dw479t1ZS4H6Y1Nvd0eneJadWOwifflXT7M_1_Xv-SJf_vrxcz5b5o2AUue0LlHJdSl5oZWyUlkkO0UsVaEI11YAtmBBArdr4NCkwlvdtKJC0kCVPM0uRt877MwmpEHCk_HozGK2NIc7DqUQhZZ7SOz5yKalbHcUB3Pvd6FP3zMAIApZCaESBSPVBB9jIPtmC9wcwjFjOCaFYw7hGJ00YtTExPa3FP5zflf0Ats0k8M</recordid><startdate>200809</startdate><enddate>200809</enddate><creator>Rozza, G.</creator><creator>Huynh, D. 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a posteriori
error estimation for linear functional outputs of affinely parametrized elliptic coercive partial differential equations. The essential ingredients are (primal-dual) Galerkin projection onto a low-dimensional space associated with a smooth “parametric manifold”—dimension reduction; efficient and effective greedy sampling methods for identification of optimal and numerically stable approximations—rapid convergence;
a posteriori
error estimation procedures—rigorous and sharp bounds for the linear-functional outputs of interest; and Offline-Online computational decomposition strategies—minimum
marginal cost
for high performance in the real-time/embedded (e.g., parameter-estimation, control) and many-query (e.g., design optimization, multi-model/scale) contexts. We present illustrative results for heat conduction and convection-diffusion, inviscid flow, and linear elasticity; outputs include transport rates, added mass, and stress intensity factors.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s11831-008-9019-9</doi><tpages>47</tpages><oa>free_for_read</oa></addata></record> |
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| source | SpringerNature Journals |
| subjects | Approximation Design optimization Engineering Engineering Sciences Mathematical and Computational Engineering Mechanics Original Paper Partial differential equations Structural mechanics Studies |
| title | Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations: Application to Transport and Continuum Mechanics |
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