Edit Profile Patera, Anthony T. Compute Distance To: Compute Author ID: patera.anthony-t Published as: Patera, A.; Patera, A. T.; Patera, Anthony; Patera, Anthony T. Documents Indexed: 133 Publications since 1981, including 1 Book all top 5 Co-Authors 4 single-authored 33 Maday, Yvon 17 Rønquist, Einar M. 12 Huynh, Dinh Bao Phuong 12 Knezevic, David J. 12 Nguyen, Ngoc Cuong 9 Yano, Masayuki 8 Peraire, Jaume 7 Eftang, Jens L. 7 Orszag, Steven Alan 6 Veroy, Karen 5 Grepl, Martin A. 5 Machiels, Luc 5 Paraschivoiu, Marius 5 Rozza, Gianluigi 5 Urban, Karsten 4 Cruz, Manuel E. 4 Fischer, Paul F. 4 Ho, Lee-Wing 4 Penn, James D. 4 Prud’homme, Christophe 4 Rovas, Dimitrios V. 4 Yeşilyurt, Serhat 3 Anagnostou, George 3 Bernardi, Christine 3 Ghaddar, Chahid K. 3 Karniadakis, George Em 3 Le Bris, Claude 3 Liu, Gui-Rong 3 Taddei, Tommaso 3 Turinici, Gabriel 2 Ballani, Jonas 2 Benner, Peter 2 Boyaval, Sébastien 2 Deville, Michel O. 2 Dewey, Daniel 2 Korczak, Karol Z. 2 Magen, Michael 2 Mavriplis, Catherine 2 Nguyen, Loi 2 Ohlberger, Mario 2 Oliveira, Ivan B. 2 Peraire, Jaime 2 Smetana, Kathrin 1 Barrault, Maxime 1 Basdevant, Claude 1 Bègue, Catherine 1 Buffa, Annalisa 1 Cancès, Eric 1 Chakir, Rachida 1 Charpentier, Isabelle 1 Chen, Yanlai 1 Dapogny, Charles 1 Debit, Naïma 1 Deparis, Simone 1 Fick, Lambert 1 Fischer, Paul E. 1 Gurfinkel Castillo, Mariano E. 1 Haasdonk, Bernard 1 Hadjiconstantinou, Nicolas G. 1 Haldenwang, Pierre 1 Hesthaven, Jan S. 1 Hoang, K. C. 1 Hussaini, M. Yousuff 1 Huynh, Phuong 1 Japhet, Caroline 1 Jung, Nadine 1 Kambourides, Miltos E. 1 Kariadakis, G. E. 1 Khoo, Boo Cheong 1 Kopriva, David Alan 1 Lacroix, J. M. 1 Lam, Khin-Yong 1 Lee, JungHyun 1 Lelièvre, Tony 1 Lewis, Robert Michael 1 Lohmann, Boris 1 Mavriplis, Cathy 1 Meiron, Dan 1 Mikic, B. B. 1 Montavon, Jean-Baptiste 1 Mula, Olga 1 Mund, Ernest H. 1 Muñoz, Rafael 1 Orlandi, Paolo 1 Otto, John 1 Ouazzani, Jalil 1 Pantz, Olivier 1 Pau, George Shu Heng 1 Pau, S. H. 1 Pedercini, Matteo 1 Peterson, John W. 1 Peyret, Roger 1 Sarrate, Josep 1 Sen, Samya 1 Sen, Sonu 1 Sorensen, Danny C. 1 Sulem, Catherine 1 Sulem, Pierre-Louis 1 Vallaghé, Sylvain 1 Yang, ZhanLu ...and 1 more Co-Authors all top 5 Serials 18 Computer Methods in Applied Mechanics and Engineering 10 Comptes Rendus. Mathématique. Académie des Sciences, Paris 8 SIAM Journal on Scientific Computing 7 Journal of Computational Physics 7 International Journal for Numerical Methods in Engineering 6 International Journal for Numerical Methods in Fluids 4 Journal of Scientific Computing 4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 4 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Journal of Fluid Mechanics 3 Archives of Computational Methods in Engineering 2 Computers and Fluids 2 International Journal of Heat and Mass Transfer 2 Mathematical and Computer Modelling of Dynamical Systems 2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 1 Communications on Pure and Applied Mathematics 1 Computers and Structures 1 Mathematics of Computation 1 Calcolo 1 Journal of Computational and Applied Mathematics 1 Mathematics and Computers in Simulation 1 Numerische Mathematik 1 Numerical Heat Transfer 1 Applied Numerical Mathematics 1 Finite Elements in Analysis and Design 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 Advances in Computational Mathematics 1 Computing and Visualization in Science 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Optimization and Engineering 1 Foundations of Computational Mathematics 1 Communications on Pure and Applied Analysis 1 Inverse Problems in Science and Engineering 1 MS&A. Modeling, Simulation and Applications all top 5 Fields 96 Numerical analysis (65-XX) 57 Partial differential equations (35-XX) 50 Fluid mechanics (76-XX) 15 Mechanics of deformable solids (74-XX) 13 Classical thermodynamics, heat transfer (80-XX) 7 Statistics (62-XX) 5 Computer science (68-XX) 5 Systems theory; control (93-XX) 4 Approximations and expansions (41-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Operations research, mathematical programming (90-XX) 2 General and overarching topics; collections (00-XX) 2 Operator theory (47-XX) 2 Probability theory and stochastic processes (60-XX) 2 Quantum theory (81-XX) 2 Biology and other natural sciences (92-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 121 Publications have been cited 3,896 times in 2,085 Documents Cited by ▼ Year ▼ A spectral element method for fluid dynamics: Laminar flow in a channel expansion. Zbl 0535.76035Patera, Anthony T. 398 1984 An ‘empirical interpolation’ method: Application to efficient reduced-basis discretization of partial differential equations. Zbl 1061.65118Barrault, Maxime; Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T. 349 2004 Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics. Zbl 1304.65251Rozza, G.; Huynh, D. B. P.; Patera, A. T. 299 2008 A new nonconforming approach to domain decomposition: The mortar element method. Zbl 0797.65094Bernardi, C.; Maday, Y.; Patera, A. T. 272 1994 Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations. Zbl 1142.65078Grepl, Martin A.; Maday, Yvon; Nguyen, Ngoc C.; Patera, Anthony T. 144 2007 Secondary instability of wall-bounded shear flows. Zbl 0556.76039Orszag, Steven A.; Patera, Anthony T. 134 1983 Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: rigorous reduced-basis a posteriori error bounds. Zbl 1134.76326Veroy, K.; Patera, A. T. 112 2005 A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations. Zbl 1079.65096Grepl, Martin A.; Patera, Anthony T. 107 2005 Domain decomposition by the mortar element method. Zbl 0799.65124Bernardi, C.; Maday, Y.; Patera, A. T. 92 1993 A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants. Zbl 1127.65086Huynh, D. B. P.; Rozza, G.; Sen, S.; Patera, A. T. 91 2007 A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations. Zbl 0907.65102Paraschivoiu, Marius; Peraire, Jaime; Patera, Anthony T. 83 1997 An operator-integration-factor splitting method for time-dependent problems: Application to incompressible fluid flow. Zbl 0724.76070Maday, Y.; Patera, Anthony T.; Rønquist, Einar M. 82 1990 A priori convergence of the greedy algorithm for the parametrized reduced basis method. Zbl 1272.65084Buffa, Annalisa; Maday, Yvon; Patera, Anthony T.; Prud’homme, Christophe; Turinici, Gabriel 65 2012 Spectral and finite difference solutions of the Burgers equations. Zbl 0612.76031Basdevant, C.; Deville, M.; Haldenwang, P.; Lacroix, J. M.; Ouazzani, J.; Peyret, R.; Orlandi, P.; Patera, A. T. 61 1986 A general multipurpose interpolation procedure: The magic points. Zbl 1184.65020Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T.; Pau, S. H. 56 2009 A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations. Zbl 1014.65115Maday, Yvon; Patera, Anthony T.; Turinici, Gabriel 47 2002 An “\(hp\)” certified reduced basis method for parametrized elliptic partial differential equations. Zbl 1228.35097Eftang, Jens L.; Patera, Anthony T.; Rønquist, Einar M. 45 2010 Analysis of iterative methods for the steady and unsteady Stokes problem: Application to spectral element discretizations. Zbl 0769.76047Maday, Yvon; Meiron, Dan; Patera, Anthony T.; Rønquist, Einar M. 45 1993 Reduced basis techniques for stochastic problems. Zbl 1269.65005Boyaval, S.; Le Bris, C.; Lelièvre, T.; Maday, Y.; Nguyen, N. C.; Patera, A. T. 44 2010 Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems. Zbl 0960.65063Machiels, Luc; Maday, Yvon; Oliveira, Ivan B.; Patera, Anthony T.; Rovas, Dimitrios V. 44 2000 Spectral element multigrid. I: Formulation and numerical results. Zbl 0666.65055Rønquist, Einar M.; Patera, Anthony T. 44 1987 An isoparametric spectral element method for solution of the Navier-Stokes equations in complex geometry. Zbl 0581.76036Korczak, Karol Z.; Patera, Anthony T. 44 1986 A ‘best points’ interpolation method for efficient approximation of parametrized functions. Zbl 1163.65009Nguyen, N. C.; Patera, A. T.; Peraire, J. 41 2008 Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation. Zbl 1178.65109Nguyen, Ngoc-Cuong; Rozza, Gianluigi; Patera, Anthony T. 40 2009 A natural-norm successive constraint method for inf-sup lower bounds. Zbl 1231.76208Huynh, D. B. P.; Knezevic, D. J.; Chen, Y.; Hesthaven, J. S.; Patera, A. T. 36 2010 “Natural norm” a posteriori error estimators for reduced basis approximations. Zbl 1100.65094Sen, S.; Veroy, K.; Huynh, D. B. P.; Deparis, S.; Nguyen, N. C.; Patera, A. T. 35 2006 A Legendre spectral element method for simulation of unsteady incompressible viscous free-surface flows. Zbl 0722.76052Ho, Lee-Wing; Patera, Anthony T. 34 1990 A static condensation reduced basis element method: approximation and a posteriori error estimation. Zbl 1276.65082Huynh, Dinh Bao Phuong; Knezevic, David J.; Patera, Anthony T. 33 2013 Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations. Zbl 1009.65066Maday, Yvon; Patera, Anthony T.; Turinici, G. 33 2002 A hierarchical duality approach to bounds for the outputs of partial differential equations. Zbl 0953.76054Paraschivoiu, Marius; Patera, Anthony T. 33 1998 Reduced-basis approximation of the viscous Burgers equation: Rigorous a posteriori error bounds. Zbl 1036.65075Veroy, Karen; Prud’homme, Christophe; Patera, Anthony T. 30 2003 A blackbox reduced-basis output bound method for noncoercive linear problems. Zbl 1006.65124Maday, Y.; Patera, A. T.; Rovas, D. V. 30 2002 Nonconforming mortar element methods: Application to spectral discretizations. Zbl 0692.65055Maday, Yvon; Mavriplis, Cathy; Patera, Anthony T. 29 1989 An improved error bound for reduced basis approximation of linear parabolic problems. Zbl 1320.65129Urban, Karsten; Patera, Anthony T. 28 2014 Numerical simulation of singular solutions to the two-dimensional cubic Schrödinger equation. Zbl 0543.65081Sulem, P. L.; Sulem, C.; Patera, A. 28 1984 Un cadre général pour l’obtention de bornes a posteriori sur des résultats en sortie d’équations aux dérivées partielles; application aux problèmes de valeurs propres. Zbl 0933.65129Maday, Yvon; Patera, Anthony T.; Peraire, Jaume 26 1999 A reduced basis approach for variational problems with stochastic parameters: application to heat conduction with variable Robin coefficient. Zbl 1230.80013Boyaval, Sébastien; Le Bris, Claude; Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T. 25 2009 An \(hp\) certified reduced basis method for parametrized parabolic partial differential equations. Zbl 1302.65223Eftang, Jens L.; Knezevic, David J.; Patera, Anthony T. 24 2011 A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics. Zbl 1352.65529Maday, Yvon; Patera, Anthony T.; Penn, James D.; Yano, Masayuki 22 2015 Reduced basis approximation and a posteriori error estimation for the parametrized unsteady Boussinesq equations. Zbl 1279.76023Knezevic, David J.; Nguyen, Ngoc-Cuong; Patera, Anthony T. 21 2011 A Legendre spectral element method for the incompressible Navier-Stokes equations. Zbl 0684.76030Rønquist, Einar M.; Patera, Anthony T. 20 1988 A Legendre spectral element method for the Stefan problem. Zbl 0632.65126Rønquist, Einar M.; Patera, Anthony T. 20 1987 Finite-amplitude stability of axisymmetric pipe flow. Zbl 0518.76037Patera, Anthony T.; Orszag, Steven A. 20 1981 A posteriori error estimation for reduced-basis approximation of parametrized elliptic coercive partial differential equations: convex inverse bound conditioners. Zbl 1092.35031Veroy, Karen; Rovas, Dimitrios V.; Patera, Anthony T. 19 2002 The generalized empirical interpolation method: stability theory on Hilbert spaces with an application to the Stokes equation. Zbl 1423.76346Maday, Y.; Mula, O.; Patera, A. T.; Yano, M. 18 2015 A posteriori error bounds for the empirical interpolation method. Zbl 1190.65018Eftang, Jens L.; Grepl, Martin A.; Patera, Anthony T. 18 2010 A “flux-free” nodal Neumann subproblem approach to output bounds for partial differential equations. Zbl 0946.65101Machiels, Luc; Maday, Yvon; Patera, Anthony T. 18 2000 Port reduction in parametrized component static condensation: approximation and a posteriori error estimation. Zbl 1352.65495Eftang, Jens L.; Patera, Anthony T. 17 2013 A new error bound for reduced basis approximation of parabolic partial differential equations. Zbl 1242.35157Urban, Karsten; Patera, Anthony T. 17 2012 Reduced basis approximation and a posteriori error estimation for stress intensity factors. Zbl 1194.74413Huynh, D. B. P.; Patera, A. T. 17 2007 A posteriori finite-element output bounds for the incompressible Navier-Stokes equations: Application to a natural convection problem. Zbl 1002.76069Machiels, L.; Peraire, J.; Patera, A. T. 17 2001 Parallel spectral element solution of the Stokes problem. Zbl 0709.76106Fischer, Paul F.; Patera, Anthony T. 17 1991 Variational formulation of three-dimensional viscous free-surface flows: Natural imposition of surface tension boundary conditions. Zbl 0739.76057Ho, Lee-Wing; Patera, Anthony T. 17 1991 A stabilized POD model for turbulent flows over a range of Reynolds numbers: optimal parameter sampling and constrained projection. Zbl 1415.76387Fick, Lambert; Maday, Yvon; Patera, Anthony T.; Taddei, Tommaso 16 2018 Asymptotic a posteriori finite element bounds for the outputs of noncoercive problems: The Helmholtz and Burgers equations. Zbl 0943.65124Peraire, Jaume; Patera, Anthony T. 16 1999 A parallel Monte Carlo finite-element procedure for the analysis of multicomponent random media. Zbl 0823.73063Cruz, Manuel E.; Patera, Anthony T. 16 1995 A space-time \(hp\)-interpolation-based certified reduced basis method for Burgers’ equation. Zbl 1295.65098Yano, Masayuki; Patera, Anthony T.; Urban, Karsten 14 2014 Reduced-basis techniques for rapid reliable optimization of systems described by affinely parametrized coercive elliptic partial differential equations. Zbl 1171.65404Oliveira, I. B.; Patera, A. T. 14 2007 Inverse identification of thermal parameters using reduced-basis method. Zbl 1137.74361Liu, G. R.; Lee, J. H.; Patera, A. T.; Yang, Z. L.; Lam, K. Y. 14 2005 A mathematical and computational framework for reliable real-time solution of parametrized partial differential equations. Zbl 1024.65104Prud’homme, Christophe; Rovas, Dimitrios V.; Veroy, Karen; Patera, Anthony T. 13 2002 A posteriori bounds for linear functional outputs of Crouzeix-Raviart finite element discretizations of the incompressible Stokes problem. Zbl 0974.76047Paraschivoiu, Marius; Patera, Anthony T. 13 2000 Parallel simulation of viscous incompressible flows. Zbl 0802.76065Fischer, Paul F.; Patera, Anthony T. 13 1994 A general output bound result: application to discretization and iteration error estimation and control. Zbl 1012.65110Patera, Anthony T.; Rønquist, Einar M. 12 2001 A certified reduced basis method for the Fokker-Planck equation of dilute polymeric fluids: FENE dumbbells in extensional flow. Zbl 1226.82051Knezevic, David J.; Patera, Anthony T. 11 2010 A posteriori finite element error bounds for nonlinear outputs of the Helmholtz equation. Zbl 0964.65119Sarrate, J.; Peraire, J.; Patera, A. 11 1999 On the mortar element method: Generalizations and implementation. Zbl 0704.65077Anagnostou, George; Maday, Yvon; Mavriplis, Catherine; Patera, Anthony T. 11 1990 Optimal local approximation spaces for component-based static condensation procedures. Zbl 1457.65216Smetana, Kathrin; Patera, Anthony T. 10 2016 PBDW state estimation: noisy observations; configuration-adaptive background spaces; physical interpretations. Zbl 1342.82116Maday, Yvon; Patera, Anthony T.; Penn, James D.; Yano, Masayuki 10 2015 A static condensation reduced basis element method: complex problems. Zbl 1286.65160Huynh, D. B. P.; Knezevic, D. J.; Patera, A. T. 10 2013 Output bounds for reduced-order approximations of elliptic partial differential equations. Zbl 0984.65118Machiels, L.; Maday, Y.; Patera, A. T. 10 2001 Numerical analysis of a posteriori finite element bounds for linear functional outputs. Zbl 1012.65109Maday, Yvon; Patera, Anthony T. 10 2000 Recent advances in parallel spectral element simulation of unsteady incompressible flows. Zbl 0668.76039Fischer, Paul F.; Ho, Lee-Wing; Karniadakis, George E.; Rønquist, Einar M.; Patera, Anthony T. 10 1988 A space-time variational approach to hydrodynamic stability theory. Zbl 1371.76054Yano, Masayuki; Patera, Anthony T. 9 2013 Certified rapid solution of partial differential equations for real-time parameter estimation and optimization. Zbl 1228.65223Grepl, Martin A.; Nguyen, Ngoc C.; Veroy, Karen; Patera, Anthony T.; Liu, Gui R. 9 2007 Reduced basis approximation and a posteriori error estimation for a Boltzmann model. Zbl 1178.76236Patera, Anthony T.; Rønquist, Einar M. 9 2007 Non-conforming spectral element-finite element approximations for partial differential equations. Zbl 0697.65080Bègue, C.; Bernardi, C.; Debit, N.; Maday, Y.; Kariadakis, G. E.; Mavriplis, C.; Patera, A. T. 9 1989 Model reduction of parametrized systems. Selected contributions based on the presentations at the MoRePaS conference, SISSA, Trieste, Italy, October 13–16, 2015. Zbl 1381.65001Benner, Peter (ed.); Ohlberger, Mario (ed.); Patera, Anthony (ed.); Rozza, Gianluigi (ed.); Urban, Karsten (ed.) 8 2017 The static condensation reduced basis element method for a mixed-mean conjugate heat exchanger model. Zbl 1298.80016Vallaghé, Sylvain; Patera, Anthony T. 8 2014 A model-data weak formulation for simultaneous estimation of state and model bias. Zbl 1281.65148Yano, Masayuki; Penn, James D.; Patera, Anthony T. 8 2013 Feasibility and competitiveness of a reduced basis approach for rapid electronic structure calculations in quantum chemistry. Zbl 1330.81022Cancès, Éric; Le Bris, Claude; Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T.; Pau, George Shu Heng 8 2007 Output bound approximations for partial differential equations; application to the incompressible Navier-Stokes equations. Zbl 0988.76052Machiels, L.; Peraire, J.; Patera, A. T. 8 1999 Fast direct Poisson solvers for high-order finite element discretizations in rectangularly decomposable domains. Zbl 0623.65111Patera, Anthony T. 8 1986 Rapid identification of material properties of the interface tissue in dental implant systems using reduced basis method. Zbl 1300.92047Hoang, K. C.; Khoo, B. C.; Liu, G. R.; Nguyen, N. C.; Patera, A. T. 7 2013 A computational procedure for part design. Zbl 0763.73079Anagnostou, George; Rønquist, Einar M.; Patera, Anthony T. 7 1992 A high-order Lagrangian-decoupling method for the incompressible Navier- Stokes equations. Zbl 0722.76038Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Rønquist, Einar M. 7 1990 Spectral collocation methods. Zbl 0671.65093Hussaini, M. Y.; Kopriva, D. A.; Patera, A. T. 7 1989 Spectral element methods: Algorithms and architectures. Zbl 0661.65107Fischer, Paul; Rønquist, Einar M.; Dewey, Daniel; Patera, Anthony T. 7 1988 A two-step certified reduced basis method. Zbl 1244.65172Eftang, J. L.; Huynh, D. B. P.; Knezevic, D. J.; Patera, A. T. 6 2012 Certified reduced basis model validation: a frequentistic uncertainty framework. Zbl 1239.93120Huynh, D. B. P.; Knezevic, D. J.; Patera, A. T. 6 2012 High-fidelity real-time simulation on deployed platforms. Zbl 1452.65429Huynh, D. B. P.; Knezevic, D. J.; Peterson, J. W.; Patera, A. T. 6 2011 Reduced-basis output bounds for approximately parametrized elliptic coercive partial differential equations. Zbl 1064.65140Prud’homme, C.; Patera, A. T. 6 2004 Approximation of parametric derivatives by the empirical interpolation method. Zbl 1284.65041Eftang, Jens L.; Grepl, Martin A.; Patera, Anthony T.; Rønquist, Einar M. 5 2013 Regression on parametric manifolds: Estimation of spatial fields, functional outputs, and parameters from noisy data. Zbl 1245.65010Patera, Anthony T.; Rønquist, Einar M. 5 2012 A general Lagrangian formulation for the computation of a posteriori finite element bounds. Zbl 1141.76426Patera, Anthony T.; Peraire, Jaume 5 2003 Fast bounds for outputs of parallel differential equations. Zbl 0924.65057Paraschivoiu, Marius; Peraire, Jaime; Maday, Yvon; Patera, Anthony T. 5 1998 Subcritical transition to turbulence in planar shear flows. Zbl 0492.76063Orszag, Steven A.; Patera, Anthony T. 5 1981 A localization strategy for data assimilation; application to state estimation and parameter estimation. Zbl 1426.65144Taddei, Tommaso; Patera, Anthony T. 4 2018 Bayesian-validated surrogates for noisy computer simulations; application to random media. Zbl 0870.65145Yeşilyurt, Serhat; Ghaddar, Chahid K.; Cruz, Manuel E.; Patera, Anthony T. 4 1996 An LP empirical quadrature procedure for parametrized functions. Zbl 1377.65074Patera, Anthony T.; Yano, Masayuki 3 2017 An \(hp\) certified reduced basis method for parametrized parabolic partial differential equations. Zbl 1216.65128Eftang, Jens L.; Patera, Anthony T.; Rønquist, Einar M. 3 2011 An LP empirical quadrature procedure for reduced basis treatment of parametrized nonlinear PDEs. Zbl 1440.65238Yano, Masayuki; Patera, Anthony T. 1 2019 Randomized residual-based error estimators for parametrized equations. Zbl 1411.65148Smetana, Kathrin; Zahm, Olivier; Patera, Anthony T. 1 2019 A stabilized POD model for turbulent flows over a range of Reynolds numbers: optimal parameter sampling and constrained projection. Zbl 1415.76387Fick, Lambert; Maday, Yvon; Patera, Anthony T.; Taddei, Tommaso 16 2018 A localization strategy for data assimilation; application to state estimation and parameter estimation. Zbl 1426.65144Taddei, Tommaso; Patera, Anthony T. 4 2018 A component-based hybrid reduced basis/finite element method for solid mechanics with local nonlinearities. Zbl 1439.74387Ballani, J.; Huynh, D. B. P.; Knezevic, D. J.; Nguyen, L.; Patera, A. T. 1 2018 Simulation-based classification; a model-order-reduction approach for structural health monitoring. Zbl 1390.74078Taddei, T.; Penn, J. D.; Yano, M.; Patera, A. T. 1 2018 Model reduction of parametrized systems. Selected contributions based on the presentations at the MoRePaS conference, SISSA, Trieste, Italy, October 13–16, 2015. Zbl 1381.65001Benner, Peter (ed.); Ohlberger, Mario (ed.); Patera, Anthony (ed.); Rozza, Gianluigi (ed.); Urban, Karsten (ed.) 8 2017 An LP empirical quadrature procedure for parametrized functions. Zbl 1377.65074Patera, Anthony T.; Yano, Masayuki 3 2017 Optimal local approximation spaces for component-based static condensation procedures. Zbl 1457.65216Smetana, Kathrin; Patera, Anthony T. 10 2016 A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics. Zbl 1352.65529Maday, Yvon; Patera, Anthony T.; Penn, James D.; Yano, Masayuki 22 2015 The generalized empirical interpolation method: stability theory on Hilbert spaces with an application to the Stokes equation. Zbl 1423.76346Maday, Y.; Mula, O.; Patera, A. T.; Yano, M. 18 2015 PBDW state estimation: noisy observations; configuration-adaptive background spaces; physical interpretations. Zbl 1342.82116Maday, Yvon; Patera, Anthony T.; Penn, James D.; Yano, Masayuki 10 2015 An improved error bound for reduced basis approximation of linear parabolic problems. Zbl 1320.65129Urban, Karsten; Patera, Anthony T. 28 2014 A space-time \(hp\)-interpolation-based certified reduced basis method for Burgers’ equation. Zbl 1295.65098Yano, Masayuki; Patera, Anthony T.; Urban, Karsten 14 2014 The static condensation reduced basis element method for a mixed-mean conjugate heat exchanger model. Zbl 1298.80016Vallaghé, Sylvain; Patera, Anthony T. 8 2014 A static condensation reduced basis element method: approximation and a posteriori error estimation. Zbl 1276.65082Huynh, Dinh Bao Phuong; Knezevic, David J.; Patera, Anthony T. 33 2013 Port reduction in parametrized component static condensation: approximation and a posteriori error estimation. Zbl 1352.65495Eftang, Jens L.; Patera, Anthony T. 17 2013 A static condensation reduced basis element method: complex problems. Zbl 1286.65160Huynh, D. B. P.; Knezevic, D. J.; Patera, A. T. 10 2013 A space-time variational approach to hydrodynamic stability theory. Zbl 1371.76054Yano, Masayuki; Patera, Anthony T. 9 2013 A model-data weak formulation for simultaneous estimation of state and model bias. Zbl 1281.65148Yano, Masayuki; Penn, James D.; Patera, Anthony T. 8 2013 Rapid identification of material properties of the interface tissue in dental implant systems using reduced basis method. Zbl 1300.92047Hoang, K. C.; Khoo, B. C.; Liu, G. R.; Nguyen, N. C.; Patera, A. T. 7 2013 Approximation of parametric derivatives by the empirical interpolation method. Zbl 1284.65041Eftang, Jens L.; Grepl, Martin A.; Patera, Anthony T.; Rønquist, Einar M. 5 2013 A priori convergence of the greedy algorithm for the parametrized reduced basis method. Zbl 1272.65084Buffa, Annalisa; Maday, Yvon; Patera, Anthony T.; Prud’homme, Christophe; Turinici, Gabriel 65 2012 A new error bound for reduced basis approximation of parabolic partial differential equations. Zbl 1242.35157Urban, Karsten; Patera, Anthony T. 17 2012 A two-step certified reduced basis method. Zbl 1244.65172Eftang, J. L.; Huynh, D. B. P.; Knezevic, D. J.; Patera, A. T. 6 2012 Certified reduced basis model validation: a frequentistic uncertainty framework. Zbl 1239.93120Huynh, D. B. P.; Knezevic, D. J.; Patera, A. T. 6 2012 Regression on parametric manifolds: Estimation of spatial fields, functional outputs, and parameters from noisy data. Zbl 1245.65010Patera, Anthony T.; Rønquist, Einar M. 5 2012 An \(hp\) certified reduced basis method for parametrized parabolic partial differential equations. Zbl 1302.65223Eftang, Jens L.; Knezevic, David J.; Patera, Anthony T. 24 2011 Reduced basis approximation and a posteriori error estimation for the parametrized unsteady Boussinesq equations. Zbl 1279.76023Knezevic, David J.; Nguyen, Ngoc-Cuong; Patera, Anthony T. 21 2011 High-fidelity real-time simulation on deployed platforms. Zbl 1452.65429Huynh, D. B. P.; Knezevic, D. J.; Peterson, J. W.; Patera, A. T. 6 2011 An \(hp\) certified reduced basis method for parametrized parabolic partial differential equations. Zbl 1216.65128Eftang, Jens L.; Patera, Anthony T.; Rønquist, Einar M. 3 2011 A Laplace transform certified reduced basis method; application to the heat equation and wave equation. Zbl 1215.65156Huynh, D. B. Phuong; Knezevic, David J.; Patera, Anthony T. 3 2011 Model order reduction and error estimation with an application to the parameter-dependent eddy current equation. Zbl 1303.93052Jung, Nadine; Patera, Anthony T.; Haasdonk, Bernard; Lohmann, Boris 2 2011 An “\(hp\)” certified reduced basis method for parametrized elliptic partial differential equations. Zbl 1228.35097Eftang, Jens L.; Patera, Anthony T.; Rønquist, Einar M. 45 2010 Reduced basis techniques for stochastic problems. Zbl 1269.65005Boyaval, S.; Le Bris, C.; Lelièvre, T.; Maday, Y.; Nguyen, N. C.; Patera, A. T. 44 2010 A natural-norm successive constraint method for inf-sup lower bounds. Zbl 1231.76208Huynh, D. B. P.; Knezevic, D. J.; Chen, Y.; Hesthaven, J. S.; Patera, A. T. 36 2010 A posteriori error bounds for the empirical interpolation method. Zbl 1190.65018Eftang, Jens L.; Grepl, Martin A.; Patera, Anthony T. 18 2010 A certified reduced basis method for the Fokker-Planck equation of dilute polymeric fluids: FENE dumbbells in extensional flow. Zbl 1226.82051Knezevic, David J.; Patera, Anthony T. 11 2010 A general multipurpose interpolation procedure: The magic points. Zbl 1184.65020Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T.; Pau, S. H. 56 2009 Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation. Zbl 1178.65109Nguyen, Ngoc-Cuong; Rozza, Gianluigi; Patera, Anthony T. 40 2009 A reduced basis approach for variational problems with stochastic parameters: application to heat conduction with variable Robin coefficient. Zbl 1230.80013Boyaval, Sébastien; Le Bris, Claude; Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T. 25 2009 Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics. Zbl 1304.65251Rozza, G.; Huynh, D. B. P.; Patera, A. T. 299 2008 A ‘best points’ interpolation method for efficient approximation of parametrized functions. Zbl 1163.65009Nguyen, N. C.; Patera, A. T.; Peraire, J. 41 2008 Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations. Zbl 1142.65078Grepl, Martin A.; Maday, Yvon; Nguyen, Ngoc C.; Patera, Anthony T. 144 2007 A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants. Zbl 1127.65086Huynh, D. B. P.; Rozza, G.; Sen, S.; Patera, A. T. 91 2007 Reduced basis approximation and a posteriori error estimation for stress intensity factors. Zbl 1194.74413Huynh, D. B. P.; Patera, A. T. 17 2007 Reduced-basis techniques for rapid reliable optimization of systems described by affinely parametrized coercive elliptic partial differential equations. Zbl 1171.65404Oliveira, I. B.; Patera, A. T. 14 2007 Certified rapid solution of partial differential equations for real-time parameter estimation and optimization. Zbl 1228.65223Grepl, Martin A.; Nguyen, Ngoc C.; Veroy, Karen; Patera, Anthony T.; Liu, Gui R. 9 2007 Reduced basis approximation and a posteriori error estimation for a Boltzmann model. Zbl 1178.76236Patera, Anthony T.; Rønquist, Einar M. 9 2007 Feasibility and competitiveness of a reduced basis approach for rapid electronic structure calculations in quantum chemistry. Zbl 1330.81022Cancès, Éric; Le Bris, Claude; Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T.; Pau, George Shu Heng 8 2007 “Natural norm” a posteriori error estimators for reduced basis approximations. Zbl 1100.65094Sen, S.; Veroy, K.; Huynh, D. B. P.; Deparis, S.; Nguyen, N. C.; Patera, A. T. 35 2006 Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: rigorous reduced-basis a posteriori error bounds. Zbl 1134.76326Veroy, K.; Patera, A. T. 112 2005 A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations. Zbl 1079.65096Grepl, Martin A.; Patera, Anthony T. 107 2005 Inverse identification of thermal parameters using reduced-basis method. Zbl 1137.74361Liu, G. R.; Lee, J. H.; Patera, A. T.; Yang, Z. L.; Lam, K. Y. 14 2005 An ‘empirical interpolation’ method: Application to efficient reduced-basis discretization of partial differential equations. Zbl 1061.65118Barrault, Maxime; Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T. 349 2004 Reduced-basis output bounds for approximately parametrized elliptic coercive partial differential equations. Zbl 1064.65140Prud’homme, C.; Patera, A. T. 6 2004 Reduced-basis approximation of the viscous Burgers equation: Rigorous a posteriori error bounds. Zbl 1036.65075Veroy, Karen; Prud’homme, Christophe; Patera, Anthony T. 30 2003 A general Lagrangian formulation for the computation of a posteriori finite element bounds. Zbl 1141.76426Patera, Anthony T.; Peraire, Jaume 5 2003 A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations. Zbl 1014.65115Maday, Yvon; Patera, Anthony T.; Turinici, Gabriel 47 2002 Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations. Zbl 1009.65066Maday, Yvon; Patera, Anthony T.; Turinici, G. 33 2002 A blackbox reduced-basis output bound method for noncoercive linear problems. Zbl 1006.65124Maday, Y.; Patera, A. T.; Rovas, D. V. 30 2002 A posteriori error estimation for reduced-basis approximation of parametrized elliptic coercive partial differential equations: convex inverse bound conditioners. Zbl 1092.35031Veroy, Karen; Rovas, Dimitrios V.; Patera, Anthony T. 19 2002 A mathematical and computational framework for reliable real-time solution of parametrized partial differential equations. Zbl 1024.65104Prud’homme, Christophe; Rovas, Dimitrios V.; Veroy, Karen; Patera, Anthony T. 13 2002 A posteriori finite-element output bounds for the incompressible Navier-Stokes equations: Application to a natural convection problem. Zbl 1002.76069Machiels, L.; Peraire, J.; Patera, A. T. 17 2001 A general output bound result: application to discretization and iteration error estimation and control. Zbl 1012.65110Patera, Anthony T.; Rønquist, Einar M. 12 2001 Output bounds for reduced-order approximations of elliptic partial differential equations. Zbl 0984.65118Machiels, L.; Maday, Y.; Patera, A. T. 10 2001 Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems. Zbl 0960.65063Machiels, Luc; Maday, Yvon; Oliveira, Ivan B.; Patera, Anthony T.; Rovas, Dimitrios V. 44 2000 A “flux-free” nodal Neumann subproblem approach to output bounds for partial differential equations. Zbl 0946.65101Machiels, Luc; Maday, Yvon; Patera, Anthony T. 18 2000 A posteriori bounds for linear functional outputs of Crouzeix-Raviart finite element discretizations of the incompressible Stokes problem. Zbl 0974.76047Paraschivoiu, Marius; Patera, Anthony T. 13 2000 Numerical analysis of a posteriori finite element bounds for linear functional outputs. Zbl 1012.65109Maday, Yvon; Patera, Anthony T. 10 2000 A posteriori finite element bounds for sensitivity derivatives of partial-differential-equation outputs. Zbl 0946.65100Lewis, Robert Michael; Patera, Anthony T.; Peraire, Jaume 3 2000 A variationally consistent finite element approach to the two-fluid internal contact-line problem. Zbl 0998.76048Hadjiconstantinou, Nicolas G.; Patera, Anthony T. 1 2000 Un cadre général pour l’obtention de bornes a posteriori sur des résultats en sortie d’équations aux dérivées partielles; application aux problèmes de valeurs propres. Zbl 0933.65129Maday, Yvon; Patera, Anthony T.; Peraire, Jaume 26 1999 Asymptotic a posteriori finite element bounds for the outputs of noncoercive problems: The Helmholtz and Burgers equations. Zbl 0943.65124Peraire, Jaume; Patera, Anthony T. 16 1999 A posteriori finite element error bounds for nonlinear outputs of the Helmholtz equation. Zbl 0964.65119Sarrate, J.; Peraire, J.; Patera, A. 11 1999 Output bound approximations for partial differential equations; application to the incompressible Navier-Stokes equations. Zbl 0988.76052Machiels, L.; Peraire, J.; Patera, A. T. 8 1999 Bounds evaluation for outputs of eigenvalue problems approximated by the overlapping modal synthesis method. Zbl 0941.65110Charpentier, Isabelle; Maday, Yvon; Patera, Anthony T. 2 1999 A hierarchical duality approach to bounds for the outputs of partial differential equations. Zbl 0953.76054Paraschivoiu, Marius; Patera, Anthony T. 33 1998 Fast bounds for outputs of parallel differential equations. Zbl 0924.65057Paraschivoiu, Marius; Peraire, Jaime; Maday, Yvon; Patera, Anthony T. 5 1998 Variational bound finite element methods for three-dimensional creeping porous media and sedimentation flows. Zbl 0910.76037Pedercini, Matteo; Patera, Anthony T.; Cruz, Manuel E. 3 1998 A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations. Zbl 0907.65102Paraschivoiu, Marius; Peraire, Jaime; Patera, Anthony T. 83 1997 Bayesian-validated computer-simulation surrogates for optimization and design: Error estimates and applications. Zbl 1017.65506Otto, John; Paraschivoiu, Marius; Yesilyurt, Serhat; Patera, Anthony T. 2 1997 Three-dimensional ribbing instability in symmetric forward-roll film-coating processes. Zbl 0892.76028Gurfinkel Castillo, Mariano E.; Patera, Anthony T. 2 1997 Bayesian-validated surrogates for noisy computer simulations; application to random media. Zbl 0870.65145Yeşilyurt, Serhat; Ghaddar, Chahid K.; Cruz, Manuel E.; Patera, Anthony T. 4 1996 A parallel Monte Carlo finite-element procedure for the analysis of multicomponent random media. Zbl 0823.73063Cruz, Manuel E.; Patera, Anthony T. 16 1995 Surrogates for numerical simulations; optimization of eddy-promoter heat exchangers. Zbl 0852.76074Yeşilyurt, Serhat; Patera, Anthony T. 3 1995 A variational-bound nip-element method for geometrically stiff problems; application to thermal composites and porous media. Zbl 0826.73076Cruz, Manuel E.; Ghaddar, Chahid K.; Patera, Anthony T. 3 1995 A new nonconforming approach to domain decomposition: The mortar element method. Zbl 0797.65094Bernardi, C.; Maday, Y.; Patera, A. T. 272 1994 Parallel simulation of viscous incompressible flows. Zbl 0802.76065Fischer, Paul F.; Patera, Anthony T. 13 1994 Domain decomposition by the mortar element method. Zbl 0799.65124Bernardi, C.; Maday, Y.; Patera, A. T. 92 1993 Analysis of iterative methods for the steady and unsteady Stokes problem: Application to spectral element discretizations. Zbl 0769.76047Maday, Yvon; Meiron, Dan; Patera, Anthony T.; Rønquist, Einar M. 45 1993 Spectral element and lattice gas methods for incompressible fluid dynamics. Zbl 1189.76379Karniadakis, George Em; Orszag, Steven A.; Rønquist, Einar M.; Patera, Anthony T. 2 1993 A general estimate for the thermal time-to-steady-state for a solid body suddenly immersed in a fluid stream. Zbl 0769.73006Maday, Y.; Patera, Anthony T. 2 1993 A computational procedure for part design. Zbl 0763.73079Anagnostou, George; Rønquist, Einar M.; Patera, Anthony T. 7 1992 Spectral element multigrid methods. Zbl 0785.65111Maday, Y.; Muñoz, R.; Patera, A.; Rønquist, E. 2 1992 Parallel spectral element solution of the Stokes problem. Zbl 0709.76106Fischer, Paul F.; Patera, Anthony T. 17 1991 Variational formulation of three-dimensional viscous free-surface flows: Natural imposition of surface tension boundary conditions. Zbl 0739.76057Ho, Lee-Wing; Patera, Anthony T. 17 1991 An operator-integration-factor splitting method for time-dependent problems: Application to incompressible fluid flow. Zbl 0724.76070Maday, Y.; Patera, Anthony T.; Rønquist, Einar M. 82 1990 A Legendre spectral element method for simulation of unsteady incompressible viscous free-surface flows. Zbl 0722.76052Ho, Lee-Wing; Patera, Anthony T. 34 1990 On the mortar element method: Generalizations and implementation. Zbl 0704.65077Anagnostou, George; Maday, Yvon; Mavriplis, Catherine; Patera, Anthony T. 11 1990 ...and 21 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,097 Authors 72 Patera, Anthony T. 59 Maday, Yvon 55 Rozza, Gianluigi 40 Quarteroni, Alfio M. 33 Karniadakis, George Em 23 Wohlmuth, Barbara I. 22 Díez, Pedro 22 Haasdonk, Bernard 22 Hesthaven, Jan S. 21 Fischer, Paul F. 21 Nguyen, Ngoc Cuong 20 Manzoni, Andrea 20 Willcox, Karen E. 19 Bernardi, Christine 19 Rønquist, Einar M. 18 Huerta, Antonio 17 Benner, Peter 17 Farhat, Charbel H. 15 Carlberg, Kevin T. 15 Chamoin, Ludovic 15 Grepl, Martin A. 15 Ladevèze, Pierre 15 Peherstorfer, Benjamin 15 Phillips, Timothy N. 15 Veroy, Karen 14 Chen, Yanlai 14 Dehghan Takht Fooladi, Mehdi 14 Ohlberger, Mario 14 Parés, Núria 14 Rapetti, Francesca 14 Urban, Karsten 14 Volkwein, Stefan 13 Abdulle, Assyr 13 Ballarin, Francesco 13 Chinesta, Francisco 13 Yano, Masayuki 12 Jiang, Lijian 12 Nouy, Anthony 11 Chen, Jinru 11 Chung, Tsz Shun Eric 11 Deville, Michel O. 11 Efendiev, Yalchin R. 11 Huynh, Dinh Bao Phuong 11 Navon, Ionel Michael 11 Peraire, Jaime 10 Amsallem, David 10 Deparis, Simone 10 Dušek, Jan 10 Giraldo, Francis X. 10 Henningson, Dan S. 10 Iliescu, Traian 10 Knezevic, David J. 10 Paraschivoiu, Marius 10 Schwab, Christoph 10 Seshaiyer, Padmanabhan 10 Stabile, Giovanni 9 Ben Belgacem, Faker 9 Bertoluzza, Silvia 9 Chen, Peng 9 Gervasio, Paola 9 Kopriva, David Alan 9 Oden, John Tinsley 9 Prud’homme, Christophe 9 Sherwin, Spencer J. 9 Wall, Wolfgang A. 9 Wheeler, Mary Fanett 8 Bordas, Stéphane Pierre Alain 8 Duczek, Sascha 8 Fang, Fangxin 8 Fidkowski, Krzysztof J. 8 Gugercin, Serkan 8 Gunzburger, Max D. 8 Hou, Thomas Yizhao 8 Li, Huiyuan 8 Li, Qiuqi 8 López, Juan Manuel 8 Marques, Francisco 8 Néron, David 8 Orszag, Steven Alan 8 Pain, Christopher C. 8 Peraire, Jaume 8 Prudhomme, Serge 8 Taddei, Tommaso 8 Yotov, Ivan 7 Alla, Alessandro 7 Babuška, Ivo 7 Barone, Matthew F. 7 Cohen, Albert 7 Eftang, Jens L. 7 Heinrichs, Wilhelm 7 Kutz, J. Nathan 7 Laursen, Tod A. 7 Luo, Zhendong 7 Minev, Peter Dimitrov 7 Narayan, Akil C. 7 Schlatter, Philipp 7 Smetana, Kathrin 7 Vohralík, Martin 6 Bar-Yoseph, Pinhas Z. 6 Chacón Rebollo, Tomás ...and 2,997 more Authors all top 5 Cited in 188 Serials 341 Computer Methods in Applied Mechanics and Engineering 265 Journal of Computational Physics 88 International Journal for Numerical Methods in Engineering 85 Journal of Fluid Mechanics 76 Computers and Fluids 75 Journal of Scientific Computing 75 SIAM Journal on Scientific Computing 53 Applied Numerical Mathematics 53 Computational Mechanics 52 Computers & Mathematics with Applications 51 Journal of Computational and Applied Mathematics 44 Physics of Fluids 37 Advances in Computational Mathematics 36 Comptes Rendus. Mathématique. 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