A Mathematical and Computational Framework for Reliable Real-Time Solution of Parametrized Partial Differential Equations
ESAIM: M2AN, 36 5 (2002) 747-771
Published online: 2002-10-15
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
91 (2024)
https://doi.org/10.1007/978-3-031-39311-2_7
5 91 (2024)
https://doi.org/10.1007/978-3-031-49892-3_10
Multi-physics model bias correction with data-driven reduced order techniques: Application to nuclear case studies
Stefano Riva, Carolina Introini and Antonio CammiApplied Mathematical Modelling 135 243 (2024)
https://doi.org/10.1016/j.apm.2024.06.040
Hybrid data assimilation methods, Part I: Numerical comparison between GEIM and PBDW
Stefano Riva, Carolina Introini, Stefano Lorenzi and Antonio CammiAnnals of Nuclear Energy 190 109864 (2023)
https://doi.org/10.1016/j.anucene.2023.109864
A reduced basis ensemble Kalman method
Francesco A. B. Silva, Cecilia Pagliantini, Martin Grepl and Karen VeroyGEM - International Journal on Geomathematics 14 (1) (2023)
https://doi.org/10.1007/s13137-023-00235-8
Data-driven reduced order modeling for parametric PDE eigenvalue problems using Gaussian process regression
Fleurianne Bertrand, Daniele Boffi and Abdul HalimJournal of Computational Physics 495 112503 (2023)
https://doi.org/10.1016/j.jcp.2023.112503
A reduced order model for the finite element approximation of eigenvalue problems
Fleurianne Bertrand, Daniele Boffi and Abdul HalimComputer Methods in Applied Mechanics and Engineering 404 115696 (2023)
https://doi.org/10.1016/j.cma.2022.115696
Hybrid Data Assimilation methods, Part II: Application to the DYNASTY experimental facility
Stefano Riva, Carolina Introini, Stefano Lorenzi and Antonio CammiAnnals of Nuclear Energy 190 109863 (2023)
https://doi.org/10.1016/j.anucene.2023.109863
Fast divergence-conforming reduced basis methods for steady Navier–Stokes flow
Eivind Fonn, Harald van Brummelen, Trond Kvamsdal and Adil RasheedComputer Methods in Applied Mechanics and Engineering 346 486 (2019)
https://doi.org/10.1016/j.cma.2018.11.038
Model order reduction for parametrized nonlinear hyperbolic problems as an application to uncertainty quantification
R. Crisovan, D. Torlo, R. Abgrall and S. TokarevaJournal of Computational and Applied Mathematics 348 466 (2019)
https://doi.org/10.1016/j.cam.2018.09.018
Hybrid hyper‐reduced modeling for contact mechanics problems
J. Fauque, I. Ramière and D. RyckelynckInternational Journal for Numerical Methods in Engineering 115 (1) 117 (2018)
https://doi.org/10.1002/nme.5798
Numerical Methods for PDEs
Daniele Antonio Di Pietro, Alexandre Ern and Luca FormaggiaSEMA SIMAI Springer Series, Numerical Methods for PDEs 15 1 (2018)
https://doi.org/10.1007/978-3-319-94676-4_1
An Adaptive Parametrized-Background Data-Weak approach to variational data assimilation
Tommaso TaddeiESAIM: Mathematical Modelling and Numerical Analysis 51 (5) 1827 (2017)
https://doi.org/10.1051/m2an/2017005
Certified reduced-order methods for optimal treatment planning
Bahodir Ahmedov, Martin A. Grepl and Michael HertyMathematical Models and Methods in Applied Sciences 26 (04) 699 (2016)
https://doi.org/10.1142/S0218202516500159
Subspace Acceleration for Large-Scale Parameter-Dependent Hermitian Eigenproblems
Petar Sirković and Daniel KressnerSIAM Journal on Matrix Analysis and Applications 37 (2) 695 (2016)
https://doi.org/10.1137/15M1017181
Reduced‐order modelling for linear heat conduction with parametrised moving heat sources
Benjamin Brands, Julia Mergheim and Paul SteinmannGAMM-Mitteilungen 39 (2) 170 (2016)
https://doi.org/10.1002/gamm.201610011
The localized reduced basis multiscale method for two‐phase flows in porous media
S. Kaulmann, B. Flemisch, B. Haasdonk, K. ‐A. Lie and M. OhlbergerInternational Journal for Numerical Methods in Engineering 102 (5) 1018 (2015)
https://doi.org/10.1002/nme.4773
A reduced basis localized orthogonal decomposition
Assyr Abdulle and Patrick HenningJournal of Computational Physics 295 379 (2015)
https://doi.org/10.1016/j.jcp.2015.04.016
Numerical analysis method of heat transfer in an electronic component using sensitivity analysis
Otmane Souhar and Christophe Prud’hommeJournal of Computational Electronics 13 (4) 1042 (2014)
https://doi.org/10.1007/s10825-014-0630-8
A static condensation reduced basis element method: Complex problems
D.B.P. Huynh, D.J. Knezevic and A.T. PateraComputer Methods in Applied Mechanics and Engineering 259 197 (2013)
https://doi.org/10.1016/j.cma.2013.02.013
Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples
Dominique Chapelle, Asven Gariah and Jacques Sainte-MarieESAIM: Mathematical Modelling and Numerical Analysis 46 (4) 731 (2012)
https://doi.org/10.1051/m2an/2011053
On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition
Toni Lassila, Andrea Manzoni and Gianluigi RozzaESAIM: Mathematical Modelling and Numerical Analysis 46 (6) 1555 (2012)
https://doi.org/10.1051/m2an/2012016
Parametric free-form shape design with PDE models and reduced basis method
Toni Lassila and Gianluigi RozzaComputer Methods in Applied Mechanics and Engineering 199 (23-24) 1583 (2010)
https://doi.org/10.1016/j.cma.2010.01.007
Reduced basis method for finite volume approximations of parametrized linear evolution equations
Bernard Haasdonk and Mario OhlbergerESAIM: Mathematical Modelling and Numerical Analysis 42 (2) 277 (2008)
https://doi.org/10.1051/m2an:2008001
Springback compensation in deep drawing applications
Flavio Cimolin, Roberto Vadori and Claudio CanutoMeccanica 43 (2) 101 (2008)
https://doi.org/10.1007/s11012-008-9117-7
Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations
G. Rozza, D. B. P. Huynh and A. T. PateraArchives of Computational Methods in Engineering 15 (3) 229 (2008)
https://doi.org/10.1007/s11831-008-9019-9
Reduced-basis techniques for rapid reliable optimization of systems described by affinely parametrized coercive elliptic partial differential equations
I. B. Oliveira and A. T. PateraOptimization and Engineering 8 (1) 43 (2007)
https://doi.org/10.1007/s11081-007-9002-6
183 (2007)
https://doi.org/10.1002/9783527611324.ch9
Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations
G. Rozza, D. B. P. Huynh and A. T. PateraArchives of Computational Methods in Engineering 15 (3) 1 (2007)
https://doi.org/10.1007/BF03024948
On the stability of the reduced basis method for Stokes equations in parametrized domains
Gianluigi Rozza and Karen VeroyComputer Methods in Applied Mechanics and Engineering 196 (7) 1244 (2007)
https://doi.org/10.1016/j.cma.2006.09.005
Numerical solution of parametrized Navier–Stokes equations by reduced basis methods
Alfio Quarteroni and Gianluigi RozzaNumerical Methods for Partial Differential Equations 23 (4) 923 (2007)
https://doi.org/10.1002/num.20249
Analysis and Simulation of Fluid Dynamics
Alf Emil Løvgren, Yvon Maday and Einar M. RønquistAnalysis and Simulation of Fluid Dynamics 129 (2006)
https://doi.org/10.1007/978-3-7643-7742-7_8
Shape Design in Aorto-Coronaric Bypass Anastomoses Using Perturbation Theory
Valery Agoshkov, Alfio Quarteroni and Gianluigi RozzaSIAM Journal on Numerical Analysis 44 (1) 367 (2006)
https://doi.org/10.1137/040613287
Reduced-basis methods for elliptic equations in sub-domains with a posteriori error bounds and adaptivity
Gianluigi RozzaApplied Numerical Mathematics 55 (4) 403 (2005)
https://doi.org/10.1016/j.apnum.2004.11.004
Handbook of Materials Modeling
Nguyen Ngoc Cuong, Karen Veroy and Anthony T. PateraHandbook of Materials Modeling 1529 (2005)
https://doi.org/10.1007/978-1-4020-3286-8_76
On optimization, control and shape design of an arterial bypass
Gianluigi RozzaInternational Journal for Numerical Methods in Fluids 47 (10-11) 1411 (2005)
https://doi.org/10.1002/fld.888