Lu, Li; Nazarov, Murtazo; Fischer, Paul Nonlinear artificial viscosity for spectral element methods. (Viscosité artificielle non linéaire pour la méthode des éléments spectraux.) (English. French summary) Zbl 1431.65188 C. R., Math., Acad. Sci. Paris 357, No. 7, 646-654 (2019). Reviewer: Hendrik Ranocha (Braunschweig) MSC: 65M70 PDFBibTeX XMLCite \textit{L. Lu} et al., C. R., Math., Acad. Sci. Paris 357, No. 7, 646--654 (2019; Zbl 1431.65188) Full Text: DOI
Bakhta, Athmane; Lombardi, Damiano An a posteriori error estimator based on shifts for positive Hermitian eigenvalue problems. (Estimateur a posteriori pour les problèmes aux valeurs propres hermitiens positifs, reposant sur des décalages.) (English. French summary) Zbl 1458.65042 C. R., Math., Acad. Sci. Paris 356, No. 6, 696-705 (2018). MSC: 65N25 65N15 PDFBibTeX XMLCite \textit{A. Bakhta} and \textit{D. Lombardi}, C. R., Math., Acad. Sci. Paris 356, No. 6, 696--705 (2018; Zbl 1458.65042) Full Text: DOI
Patera, Anthony T.; Yano, Masayuki An LP empirical quadrature procedure for parametrized functions. (Une procédure de quadrature empirique par programmation linéaire pour les fonctions à paramètres.) (English. French summary) Zbl 1377.65074 C. R., Math., Acad. Sci. Paris 355, No. 11, 1161-1167 (2017). MSC: 65K10 49J20 49M37 90C34 49M30 90C05 PDFBibTeX XMLCite \textit{A. T. Patera} and \textit{M. Yano}, C. R., Math., Acad. Sci. Paris 355, No. 11, 1161--1167 (2017; Zbl 1377.65074) Full Text: DOI
O’Connor, Robert A successive constraint approach to solving parameter-dependent linear matrix inequalities. (Une méthode de contraintes successives pour résoudre les inégalités matricielles linéaires paramétriques.) (English. French summary) Zbl 1369.65061 C. R., Math., Acad. Sci. Paris 355, No. 6, 723-728 (2017). MSC: 65F30 15A39 90C22 65K05 PDFBibTeX XMLCite \textit{R. O'Connor}, C. R., Math., Acad. Sci. Paris 355, No. 6, 723--728 (2017; Zbl 1369.65061) Full Text: DOI arXiv
Azaïez, Mejdi; Ben Belgacem, Faker; Chacón Rebollo, Tomás; Gómez Mármol, Macarena; Sánchez Muñoz, Isabel Error bounds in high-order Sobolev norms for POD expansions of parameterized transient temperatures. (Estimations d’erreur d’ordre élevé pour la décomposition POD appliquée à l’équation de la chaleur parametrisée.) (English. Abridged French version) Zbl 1362.65095 C. R., Math., Acad. Sci. Paris 355, No. 4, 432-438 (2017). MSC: 65M15 65M12 65M60 35K05 PDFBibTeX XMLCite \textit{M. Azaïez} et al., C. R., Math., Acad. Sci. Paris 355, No. 4, 432--438 (2017; Zbl 1362.65095) Full Text: DOI
O’Connor, Robert Bounding stability constants for affinely parameter-dependent operators. (Des bornes inférieures pour les constantes de stabilité associées à des operateurs avec une dépendance affine des paramètres.) (English. French summary) Zbl 1353.65111 C. R., Math., Acad. Sci. Paris 354, No. 12, 1236-1240 (2016). MSC: 65N12 35G20 65N15 65N30 PDFBibTeX XMLCite \textit{R. O'Connor}, C. R., Math., Acad. Sci. Paris 354, No. 12, 1236--1240 (2016; Zbl 1353.65111) Full Text: DOI arXiv
Choulli, Mourad; Zuazua, Enrique Lipschitz dependence of the coefficients on the resolvent and greedy approximation for scalar elliptic problems. (Dépendance Lipschitz des coefficients comme fonction de la résolvante et approximation greedy pour les problèmes elliptiques scalaires.) (English. French summary) Zbl 1349.35426 C. R., Math., Acad. Sci. Paris 354, No. 12, 1174-1187 (2016). MSC: 35R30 35J05 PDFBibTeX XMLCite \textit{M. Choulli} and \textit{E. Zuazua}, C. R., Math., Acad. Sci. Paris 354, No. 12, 1174--1187 (2016; Zbl 1349.35426) Full Text: DOI arXiv
Daversin, Cécile; Prud’homme, Christophe Simultaneous empirical interpolation and reduced basis method for non-linear problems. (Une méthode EIM bases réduites simultanée pour les équations aux dérivées partielles non linéaires et non affines.) (English. French summary) Zbl 1382.65386 C. R., Math., Acad. Sci. Paris 353, No. 12, 1105-1109 (2015). MSC: 65N30 PDFBibTeX XMLCite \textit{C. Daversin} and \textit{C. Prud'homme}, C. R., Math., Acad. Sci. Paris 353, No. 12, 1105--1109 (2015; Zbl 1382.65386) Full Text: DOI arXiv
Abdulle, Assyr; Budáč, Ondrej A Petrov-Galerkin reduced basis approximation of the Stokes equation in parameterized geometries. (Une méthode d’éléments finis de type Petrov-Galerkin pour l’approximation en base réduite du probléme de Stokes.) (English. Abridged French version) Zbl 1320.76057 C. R., Math., Acad. Sci. Paris 353, No. 7, 641-645 (2015). MSC: 76M10 65N30 65N12 76D07 PDFBibTeX XMLCite \textit{A. Abdulle} and \textit{O. Budáč}, C. R., Math., Acad. Sci. Paris 353, No. 7, 641--645 (2015; Zbl 1320.76057) Full Text: DOI
Chen, Yanlai; Gottlieb, Sigal; Maday, Yvon Parametric analytical preconditioning and its applications to the reduced collocation methods. (Préconditionnements analytiques en paramètres et applications aux méthodes de collocation réduites.) (English. French summary) Zbl 1297.65166 C. R., Math., Acad. Sci. Paris 352, No. 7-8, 661-666 (2014). MSC: 65N35 35J25 65N15 65F08 65N12 PDFBibTeX XMLCite \textit{Y. Chen} et al., C. R., Math., Acad. Sci. Paris 352, No. 7--8, 661--666 (2014; Zbl 1297.65166) Full Text: DOI arXiv
Jäggli, Christoph; Iapichino, Laura; Rozza, Gianluigi An improvement on geometrical parameterizations by transfinite maps. (Une amélioration pour les paramétrages géometriques par les transformations transfinies.) (English. Abridged French version) Zbl 1302.35167 C. R., Math., Acad. Sci. Paris 352, No. 3, 263-268 (2014). MSC: 35J57 35J05 65N99 PDFBibTeX XMLCite \textit{C. Jäggli} et al., C. R., Math., Acad. Sci. Paris 352, No. 3, 263--268 (2014; Zbl 1302.35167) Full Text: DOI Link
Yano, Masayuki; Penn, James D.; Patera, Anthony T. A model-data weak formulation for simultaneous estimation of state and model bias. (Estimation de la variable d’état et du biais de modèle par une formulation faible incorporant les données.) (English. French summary) Zbl 1281.65148 C. R., Math., Acad. Sci. Paris 351, No. 23-24, 937-941 (2013). MSC: 65N30 65N15 35J05 PDFBibTeX XMLCite \textit{M. Yano} et al., C. R., Math., Acad. Sci. Paris 351, No. 23--24, 937--941 (2013; Zbl 1281.65148) Full Text: DOI Link
Ohlberger, Mario; Rave, Stephan Nonlinear reduced basis approximation of parameterized evolution equations via the method of freezing. (Approximation non linéaire utilisant des bases réduites d’équations d’évolution paramétrées par une méthode de figeage.) (English. Abridged French version) Zbl 1281.65117 C. R., Math., Acad. Sci. Paris 351, No. 23-24, 901-906 (2013). MSC: 65M08 35Q53 PDFBibTeX XMLCite \textit{M. Ohlberger} and \textit{S. Rave}, C. R., Math., Acad. Sci. Paris 351, No. 23--24, 901--906 (2013; Zbl 1281.65117) Full Text: DOI arXiv
Devaud, Denis; Manzoni, Andrea; Rozza, Gianluigi A combination between the reduced basis method and the ANOVA expansion: on the computation of sensitivity indices. (English. French summary) Zbl 1279.65137 C. R., Math., Acad. Sci. Paris 351, No. 15-16, 593-598 (2013). MSC: 65N99 35J60 PDFBibTeX XMLCite \textit{D. Devaud} et al., C. R., Math., Acad. Sci. Paris 351, No. 15--16, 593--598 (2013; Zbl 1279.65137) Full Text: DOI
Patera, Anthony T.; Rønquist, Einar M. Regression on parametric manifolds: Estimation of spatial fields, functional outputs, and parameters from noisy data. (English. Abridged French version) Zbl 1245.65010 C. R., Math., Acad. Sci. Paris 350, No. 9-10, 543-547 (2012). MSC: 65C60 62F10 62J05 62F25 PDFBibTeX XMLCite \textit{A. T. Patera} and \textit{E. M. Rønquist}, C. R., Math., Acad. Sci. Paris 350, No. 9--10, 543--547 (2012; Zbl 1245.65010) Full Text: DOI Link
Casenave, Fabien Accurate a posteriori error evaluation in the reduced basis method. (English. French summary) Zbl 1245.65105 C. R., Math., Acad. Sci. Paris 350, No. 9-10, 539-542 (2012). MSC: 65L70 65L10 34B05 PDFBibTeX XMLCite \textit{F. Casenave}, C. R., Math., Acad. Sci. Paris 350, No. 9--10, 539--542 (2012; Zbl 1245.65105) Full Text: DOI arXiv
Urban, Karsten; Patera, Anthony T. A new error bound for reduced basis approximation of parabolic partial differential equations. (English. Abridged French version) Zbl 1242.35157 C. R., Math., Acad. Sci. Paris 350, No. 3-4, 203-207 (2012). Reviewer: Alain Brillard (Riedisheim) MSC: 35K90 47F05 49M27 65N15 PDFBibTeX XMLCite \textit{K. Urban} and \textit{A. T. Patera}, C. R., Math., Acad. Sci. Paris 350, No. 3--4, 203--207 (2012; Zbl 1242.35157) Full Text: DOI Link
Grepl, Martin A.; Veroy, Karen A level set reduced basis approach to parameter estimation. (English. French summary) Zbl 1269.65115 C. R., Math., Acad. Sci. Paris 349, No. 23-24, 1229-1232 (2011). MSC: 65N21 35R30 35J05 PDFBibTeX XMLCite \textit{M. A. Grepl} and \textit{K. Veroy}, C. R., Math., Acad. Sci. Paris 349, No. 23--24, 1229--1232 (2011; Zbl 1269.65115) Full Text: DOI Link
Grepl, Martin A.; Kärcher, Mark Reduced basis a posteriori error bounds for parametrized linear-quadratic elliptic optimal control problems. (English. Abridged French version) Zbl 1232.49039 C. R., Math., Acad. Sci. Paris 349, No. 15-16, 873-877 (2011). MSC: 49N10 49M30 49K20 PDFBibTeX XMLCite \textit{M. A. Grepl} and \textit{M. Kärcher}, C. R., Math., Acad. Sci. Paris 349, No. 15--16, 873--877 (2011; Zbl 1232.49039) Full Text: DOI
Huynh, D. B. Phuong; Knezevic, David J.; Patera, Anthony T. A Laplace transform certified reduced basis method; application to the heat equation and wave equation. (Une méthode de bases réduites certifiée utilisant la transformation de Laplace; Application à l’équation de la chaleur et à l’équation des ondes.) (English. Abridged French version) Zbl 1215.65156 C. R., Math., Acad. Sci. Paris 349, No. 7-8, 401-405 (2011). MSC: 65M38 35K05 35L05 35A22 44A10 65M15 PDFBibTeX XMLCite \textit{D. B. P. Huynh} et al., C. R., Math., Acad. Sci. Paris 349, No. 7--8, 401--405 (2011; Zbl 1215.65156) Full Text: DOI Link
Lassila, Toni; Rozza, Gianluigi Model reduction of semiaffinely parameterized partial differential equations by two-level affine approximation. (Réduction de modèle pour des équations aux dérivées partielles paramétrisées semi-affinement par une approximation affine à deux niveaux.) (English. Abridged French version) Zbl 1211.35019 C. R., Math., Acad. Sci. Paris 349, No. 1-2, 61-66 (2011). MSC: 35A35 65M15 PDFBibTeX XMLCite \textit{T. Lassila} and \textit{G. Rozza}, C. R., Math., Acad. Sci. Paris 349, No. 1--2, 61--66 (2011; Zbl 1211.35019) Full Text: DOI Link
Eftang, Jens L.; Grepl, Martin A.; Patera, Anthony T. A posteriori error bounds for the empirical interpolation method. (English. Abridged French version) Zbl 1190.65018 C. R., Math., Acad. Sci. Paris 348, No. 9-10, 575-579 (2010). MSC: 65D05 41A05 PDFBibTeX XMLCite \textit{J. L. Eftang} et al., C. R., Math., Acad. Sci. Paris 348, No. 9--10, 575--579 (2010; Zbl 1190.65018) Full Text: DOI Link
Chakir, Rachida; Maday, Yvon A two-grid finite-element/reduced basis scheme for the approximation of the solution of parametric dependent P.D.E. (Une méthode combinée d’éléments finis à deux grilles/bases réduites pour l’approximation des solutions d’une E.D.P. Paramétrique.) (French. Abridged English version) Zbl 1161.65083 C. R., Math., Acad. Sci. Paris 347, No. 7-8, 435-440 (2009). MSC: 65N30 35J25 35J65 65N12 65N15 PDFBibTeX XMLCite \textit{R. Chakir} and \textit{Y. Maday}, C. R., Math., Acad. Sci. Paris 347, No. 7--8, 435--440 (2009; Zbl 1161.65083) Full Text: DOI
Chen, Yanlai; Hesthaven, Jan S.; Maday, Yvon; Rodríguez, Jerónimo A monotonic evaluation of lower bounds for inf-sup stability constants in the frame of reduced basis approximations. (English. Abridged French version) Zbl 1152.65109 C. R., Math., Acad. Sci. Paris 346, No. 23-24, 1295-1300 (2008). MSC: 65N30 65N12 PDFBibTeX XMLCite \textit{Y. Chen} et al., C. R., Math., Acad. Sci. Paris 346, No. 23--24, 1295--1300 (2008; Zbl 1152.65109) Full Text: DOI
Maday, Yvon; Razafison, Ulrich A reduced basis method applied to the restricted Hartree-Fock equations. (English) Zbl 1133.81063 C. R., Math., Acad. Sci. Paris 346, No. 3-4, 243-248 (2008). MSC: 81V55 81-04 PDFBibTeX XMLCite \textit{Y. Maday} and \textit{U. Razafison}, C. R., Math., Acad. Sci. Paris 346, No. 3--4, 243--248 (2008; Zbl 1133.81063) Full Text: DOI
Huynh, D. B. P.; Rozza, G.; Sen, S.; Patera, A. T. A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants. (English) Zbl 1127.65086 C. R., Math., Acad. Sci. Paris 345, No. 8, 473-478 (2007). MSC: 65N30 35J05 65N12 74B05 74S05 76Q05 76M10 PDFBibTeX XMLCite \textit{D. B. P. Huynh} et al., C. R., Math., Acad. Sci. Paris 345, No. 8, 473--478 (2007; Zbl 1127.65086) Full Text: DOI
Barrault, Maxime; Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T. An ‘empirical interpolation’ method: Application to efficient reduced-basis discretization of partial differential equations. (English. Abridged French version) Zbl 1061.65118 C. R., Math., Acad. Sci. Paris 339, No. 9, 667-672 (2004). MSC: 65N21 35J25 65N30 65N15 35R30 PDFBibTeX XMLCite \textit{M. Barrault} et al., C. R., Math., Acad. Sci. Paris 339, No. 9, 667--672 (2004; Zbl 1061.65118) Full Text: DOI
Stefanica, Dan Lower bounds for additive Schwarz methods with mortars. (English. Abridged French version) Zbl 1061.65137 C. R., Math., Acad. Sci. Paris 339, No. 10, 739-743 (2004). MSC: 65N55 65F10 65F35 65N30 35J25 PDFBibTeX XMLCite \textit{D. Stefanica}, C. R., Math., Acad. Sci. Paris 339, No. 10, 739--743 (2004; Zbl 1061.65137) Full Text: DOI
Glowinski, Roland; He, Jiwen; Rappaz, Jacques; Wagner, Joël A multi-domain method for solving numerically multi-scale elliptic problems. (English) Zbl 1049.65145 C. R., Math., Acad. Sci. Paris 338, No. 9, 741-746 (2004). MSC: 65N55 35J05 65N30 65F10 PDFBibTeX XMLCite \textit{R. Glowinski} et al., C. R., Math., Acad. Sci. Paris 338, No. 9, 741--746 (2004; Zbl 1049.65145) Full Text: DOI
Bertoluzza, Silvia; Piquemal, Anne-Sophie The wavelet Mortar method in the adaptative framework. (English) Zbl 1049.65142 C. R., Math., Acad. Sci. Paris 338, No. 8, 653-656 (2004). MSC: 65N55 65N30 35J05 65T60 65N12 PDFBibTeX XMLCite \textit{S. Bertoluzza} and \textit{A.-S. Piquemal}, C. R., Math., Acad. Sci. Paris 338, No. 8, 653--656 (2004; Zbl 1049.65142) Full Text: DOI
Saas, Laurent; Faille, Isabelle; Nataf, Frédéric; Willien, Françoise Domain decomposition for a finite volume method on non-matching grids. (English. Abridged French version) Zbl 1038.65136 C. R., Math., Acad. Sci. Paris 338, No. 5, 407-412 (2004). MSC: 65N55 65N30 65N15 35J25 PDFBibTeX XMLCite \textit{L. Saas} et al., C. R., Math., Acad. Sci. Paris 338, No. 5, 407--412 (2004; Zbl 1038.65136) Full Text: DOI
Bourgault, Yves; El Boukili, Abderrazzak A mortar element method for hyperbolic problems. (English. Abridged French version) Zbl 1038.65094 C. R., Math., Acad. Sci. Paris 338, No. 3, 249-254 (2004). MSC: 65M60 65M55 65M50 35L45 PDFBibTeX XMLCite \textit{Y. Bourgault} and \textit{A. El Boukili}, C. R., Math., Acad. Sci. Paris 338, No. 3, 249--254 (2004; Zbl 1038.65094) Full Text: DOI
Veroy, Karen; Prud’homme, Christophe; Patera, Anthony T. Reduced-basis approximation of the viscous Burgers equation: Rigorous a posteriori error bounds. (English. Abridged French version) Zbl 1036.65075 C. R., Math., Acad. Sci. Paris 337, No. 9, 619-624 (2003). MSC: 65M15 35J65 35Q53 65M12 65M60 PDFBibTeX XMLCite \textit{K. Veroy} et al., C. R., Math., Acad. Sci. Paris 337, No. 9, 619--624 (2003; Zbl 1036.65075) Full Text: DOI
Maday, Yvon; Patera, Anthony T.; Turinici, G. Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations. (English. Abridged French version) Zbl 1009.65066 C. R., Math., Acad. Sci. Paris 335, No. 3, 289-294 (2002). MSC: 65N12 35J25 65N30 PDFBibTeX XMLCite \textit{Y. Maday} et al., C. R., Math., Acad. Sci. Paris 335, No. 3, 289--294 (2002; Zbl 1009.65066) Full Text: DOI
Maday, Yvon; Rønquist, Einar M. A reduced-basis element method. (English. Abridged French version) Zbl 1006.65128 C. R., Math., Acad. Sci. Paris 335, No. 2, 195-200 (2002). MSC: 65N30 35J05 76M10 92C35 76Z05 65Y20 PDFBibTeX XMLCite \textit{Y. Maday} and \textit{E. M. Rønquist}, C. R., Math., Acad. Sci. Paris 335, No. 2, 195--200 (2002; Zbl 1006.65128) Full Text: DOI
Maday, Yvon; Rapetti, Francesca; Wohlmuth, Barbara I. Coupling between scalar and vector potentials by the mortar element method. (English. Abridged French version) Zbl 1002.65130 C. R., Math., Acad. Sci. Paris 334, No. 10, 933-938 (2002). MSC: 65N30 35Q60 78A25 78M10 PDFBibTeX XMLCite \textit{Y. Maday} et al., C. R., Math., Acad. Sci. Paris 334, No. 10, 933--938 (2002; Zbl 1002.65130) Full Text: DOI