Taddei, T.; Penn, J. D.; Yano, M.; Patera, A. T. Simulation-based classification; a model-order-reduction approach for structural health monitoring. (English) Zbl 1390.74078 Arch. Comput. Methods Eng. 25, No. 1, 23-45 (2018). MSC: 74G75 62H30 74S60 62P35 PDFBibTeX XMLCite \textit{T. Taddei} et al., Arch. Comput. Methods Eng. 25, No. 1, 23--45 (2018; Zbl 1390.74078) Full Text: DOI Link
Boyaval, S.; Le Bris, C.; Lelièvre, T.; Maday, Y.; Nguyen, N. C.; Patera, A. T. Reduced basis techniques for stochastic problems. (English) Zbl 1269.65005 Arch. Comput. Methods Eng. 17, No. 4, 435-454 (2010). MSC: 65C30 35R60 60H25 62F15 PDFBibTeX XMLCite \textit{S. Boyaval} et al., Arch. Comput. Methods Eng. 17, No. 4, 435--454 (2010; Zbl 1269.65005) Full Text: DOI arXiv
Boyaval, Sébastien; Le Bris, Claude; Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T. A reduced basis approach for variational problems with stochastic parameters: application to heat conduction with variable Robin coefficient. (English) Zbl 1230.80013 Comput. Methods Appl. Mech. Eng. 198, No. 41-44, 3187-3206 (2009). MSC: 80M31 80A20 65C30 65C05 PDFBibTeX XMLCite \textit{S. Boyaval} et al., Comput. Methods Appl. Mech. Eng. 198, No. 41--44, 3187--3206 (2009; Zbl 1230.80013) Full Text: DOI Link
Rozza, G.; Huynh, D. B. P.; Patera, A. T. Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics. (English) Zbl 1304.65251 Arch. Comput. Methods Eng. 15, No. 3, 229-275 (2008). MSC: 65N30 74S05 65N15 76M10 PDFBibTeX XMLCite \textit{G. Rozza} et al., Arch. Comput. Methods Eng. 15, No. 3, 229--275 (2008; Zbl 1304.65251) Full Text: DOI
Patera, Anthony T.; Rønquist, Einar M. A general output bound result: application to discretization and iteration error estimation and control. (English) Zbl 1012.65110 Math. Models Methods Appl. Sci. 11, No. 4, 685-712 (2001). MSC: 65N15 65N55 65N30 35J05 65F10 65F35 PDFBibTeX XMLCite \textit{A. T. Patera} and \textit{E. M. Rønquist}, Math. Models Methods Appl. Sci. 11, No. 4, 685--712 (2001; Zbl 1012.65110) Full Text: DOI
Machiels, L.; Peraire, J.; Patera, A. T. A posteriori finite-element output bounds for the incompressible Navier-Stokes equations: Application to a natural convection problem. (English) Zbl 1002.76069 J. Comput. Phys. 172, No. 2, 401-425 (2001). MSC: 76M10 76D05 76R10 80A20 65N15 PDFBibTeX XMLCite \textit{L. Machiels} et al., J. Comput. Phys. 172, No. 2, 401--425 (2001; Zbl 1002.76069) Full Text: DOI
Machiels, L.; Maday, Y.; Patera, A. T. Output bounds for reduced-order approximations of elliptic partial differential equations. (English) Zbl 0984.65118 Comput. Methods Appl. Mech. Eng. 190, No. 26-27, 3413-3426 (2001). MSC: 65N30 65N12 65N15 35J25 80A20 80M10 PDFBibTeX XMLCite \textit{L. Machiels} et al., Comput. Methods Appl. Mech. Eng. 190, No. 26--27, 3413--3426 (2001; Zbl 0984.65118) Full Text: DOI
Maday, Yvon; Patera, Anthony T. Numerical analysis of a posteriori finite element bounds for linear functional outputs. (English) Zbl 1012.65109 Math. Models Methods Appl. Sci. 10, No. 5, 785-799 (2000). MSC: 65N15 65N30 35J25 PDFBibTeX XMLCite \textit{Y. Maday} and \textit{A. T. Patera}, Math. Models Methods Appl. Sci. 10, No. 5, 785--799 (2000; Zbl 1012.65109) Full Text: DOI
Sarrate, J.; Peraire, J.; Patera, A. A posteriori finite element error bounds for nonlinear outputs of the Helmholtz equation. (English) Zbl 0964.65119 Int. J. Numer. Methods Fluids 31, No. 1, 17-36 (1999). MSC: 65N15 65N30 35J05 PDFBibTeX XMLCite \textit{J. Sarrate} et al., Int. J. Numer. Methods Fluids 31, No. 1, 17--36 (1999; Zbl 0964.65119) Full Text: DOI
Peraire, Jaume; Patera, Anthony T. Asymptotic a posteriori finite element bounds for the outputs of noncoercive problems: The Helmholtz and Burgers equations. (English) Zbl 0943.65124 Comput. Methods Appl. Mech. Eng. 171, No. 1-2, 77-86 (1999). Reviewer: Thomas Sonar (Braunschweig) MSC: 65N15 65N30 35J65 35Q53 PDFBibTeX XMLCite \textit{J. Peraire} and \textit{A. T. Patera}, Comput. Methods Appl. Mech. Eng. 171, No. 1--2, 77--86 (1999; Zbl 0943.65124) Full Text: DOI
Paraschivoiu, Marius; Patera, Anthony T. A hierarchical duality approach to bounds for the outputs of partial differential equations. (English) Zbl 0953.76054 Comput. Methods Appl. Mech. Eng. 158, No. 3-4, 389-407 (1998). MSC: 76M10 76R99 65N30 65N15 PDFBibTeX XMLCite \textit{M. Paraschivoiu} and \textit{A. T. Patera}, Comput. Methods Appl. Mech. Eng. 158, No. 3--4, 389--407 (1998; Zbl 0953.76054) Full Text: DOI
Paraschivoiu, Marius; Peraire, Jaime; Patera, Anthony T. A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations. (English) Zbl 0907.65102 Comput. Methods Appl. Mech. Eng. 150, No. 1-4, 289-312 (1997). MSC: 65N15 65N30 35J25 PDFBibTeX XMLCite \textit{M. Paraschivoiu} et al., Comput. Methods Appl. Mech. Eng. 150, No. 1--4, 289--312 (1997; Zbl 0907.65102) Full Text: DOI