Edit Profile (opens in new tab) Bernardi, Christine Compute Distance To: Compute Author ID: bernardi.christine Published as: Bernardi, Christine; Bernardi, C. External Links: MGP · ORCID · Wikidata · ResearchGate · dblp · GND · IdRef · theses.fr Documents Indexed: 166 Publications since 1981, including 3 Books 1 Contribution as Editor Co-Authors: 90 Co-Authors with 161 Joint Publications 2,111 Co-Co-Authors all top 5 Co-Authors 6 single-authored 40 Maday, Yvon 22 Hecht, Frédéric 16 Ben Belgacem, Faker 15 Girault, Vivette 13 Chacón Rebollo, Tomás 10 Blouza, Adel 10 Dauge, Monique 8 Azaïez, Mejdi 8 Belhachmi, Zakaria 7 Chorfi, Nejmeddine 7 Karageorghis, Andreas 7 Métivet, Brigitte 6 Amara, Mohamed 6 Lewandowski, Roger 6 Murat, François 6 Pironneau, Olivier 6 Sayah, Toni 6 Yakoubi, Driss 5 Mghazli, Zoubida 5 Raugel, Geneviève 4 Canuto, Claudio 4 Chacón Vera, Eliseo 4 Verfürth, Rüdiger 3 Costabel, Martin 3 Dakroub, Jad 3 Debit, Naïma 3 Deparis, Simone 3 El Alaoui, Linda 3 Maarouf, Sarra 3 Mansour, Gihane 3 Orfi, Ajmia Younes 3 Patera, Anthony T. 3 Rapetti, Francesca 3 Satouri, Jamil 3 Vohralík, Martin 2 Achdou, Yves 2 Agroum, Rahma 2 Amoura, Karima 2 Aouadi, Saloua Mani 2 Bergam, Amal 2 Coppoletta, Giuseppe 2 Gómez Mármol, Macarena 2 Pelissier, Marie-Claude 2 Pernaud-Thomas, Bernadette 1 Abdellatif, Nahla 1 Abdellatif, Nehla 1 Ahusborde, Etienne 1 Amorim, Paulo 1 Amrouche, Chérif 1 Antidze, J. 1 Avalishvili, Gia 1 Avalishvili, Mariam 1 Bègue, Catherine 1 Benyounes, Michèle 1 Borchorishvili, R. 1 Bristeau, Marie-Odile 1 Chacon, Tomas 1 Copetti, Maria Inês M. 1 Coquel, Frédéric 1 Coronil, D. Franco 1 Dib, Séréna 1 El Fekih, Henda 1 El Rhabi, Mohammed 1 Fiétier, Nicolas 1 Godlewski, Edwige 1 Grundmann, Miloslav 1 Halpern, Laurence 1 Jelassi, Faten 1 Karniadakis, George Em 1 Kawarada, Hideo 1 Kharrat, Nizar 1 Laval, Frédéric 1 Le Dret, Hervé 1 LeFloch, Philippe Gerard 1 Mint Brahim, Maimouna 1 Moussaoui, Mohand-Arezki 1 Nouri, Fatma Zohra 1 1 Owens, Robert G. 1 Rafei, Farah 1 Rajagopal, Kumbakonam Ramamani 1 Rappaz, Jacques 1 Restelli, Marco 1 Saadi, Samira 1 Sacchi Landriani, Giovanni 1 Salmon, Stéphanie 1 Süli, Endre E. 1 Taallah, Frekh 1 Touihri, Moncef 1 Vallet, Marie-Gabrielle 1 Younes, M. Ben all top 5 Serials 15 SIAM Journal on Numerical Analysis 12 IMA Journal of Numerical Analysis 11 Numerische Mathematik 10 Comptes Rendus de l’Académie des Sciences. Série I 10 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 9 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 7 Computer Methods in Applied Mechanics and Engineering 7 Mathematics of Computation 5 Journal of Scientific Computing 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 S\(\vec{\text{e}}\)MA Journal 4 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 3 Mathematical Methods in the Applied Sciences 3 Calcolo 3 Applied Numerical Mathematics 3 RAIRO. Modélisation Mathématique et Analyse Numérique 3 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 2 Applicable Analysis 2 International Journal for Numerical Methods in Fluids 2 Applied Mathematics and Computation 2 Chinese Annals of Mathematics. Series B 2 Journal of Elasticity 2 East-West Journal of Numerical Mathematics 2 Revue Européenne des Éléments Finis 2 Journal of Mathematical Fluid Mechanics 2 Mathématiques & Applications (Berlin) 1 Classical and Quantum Gravity 1 Computers & Mathematics with Applications 1 Computers and Structures 1 Journal of Computational and Applied Mathematics 1 RAIRO. Analyse Numérique 1 Finite Elements in Analysis and Design 1 Numerical Methods for Partial Differential Equations 1 Asymptotic Analysis 1 Numerical Algorithms 1 Communications in Partial Differential Equations 1 La Recherche Aérospatiale 1 SIAM Journal on Mathematical Analysis 1 Applied Mathematics and Informatics 1 Bulletin of TICMI 1 GAMM-Mitteilungen 1 Mathematical Modelling of Natural Phenomena 1 Advances in Pure and Applied Mathematics 1 Nonlinear Analysis. Theory, Methods & Applications all top 5 Fields 134 Numerical analysis (65-XX) 96 Partial differential equations (35-XX) 84 Fluid mechanics (76-XX) 9 Functional analysis (46-XX) 8 Mechanics of deformable solids (74-XX) 6 Approximations and expansions (41-XX) 4 Optics, electromagnetic theory (78-XX) 4 Geophysics (86-XX) 3 Potential theory (31-XX) 3 Ordinary differential equations (34-XX) 3 Operator theory (47-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 General and overarching topics; collections (00-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Convex and discrete geometry (52-XX) 1 Relativity and gravitational theory (83-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 149 Publications have been cited 2,768 times in 2,032 Documents Cited by ▼ Year ▼ Vector potentials in three-dimensional non-smooth domains. Zbl 0914.35094Amrouche, C.; Bernardi, C.; Dauge, M.; Girault, V. 380 1998 A new nonconforming approach to domain decomposition: The mortar element method. Zbl 0797.65094Bernardi, C.; Maday, Y.; Patera, A. T. 275 1994 Spectral approximation for elliptic boundary value problems. (Approximations spectrales de problèmes aux limites elliptiques.) Zbl 0773.47032Bernardi, Christine; Maday, Yvon 137 1992 Domain decomposition by the mortar element method. Zbl 0799.65124Bernardi, C.; Maday, Y.; Patera, A. T. 102 1993 Analysis of some finite elements for the Stokes problem. Zbl 0563.65075Bernardi, Christine; Raugel, Geneviève 88 1985 Adaptive finite element methods for elliptic equations with non-smooth coefficients. Zbl 0962.65096Bernardi, C.; Verfürth, R. 85 2000 A local regularization operator for triangular and quadrilateral finite elements. Zbl 0913.65007Bernardi, C.; Girault, V. 85 1998 Optimal finite-element interpolation on curved domains. Zbl 0678.65003Bernardi, Christine 84 1989 Generalized inf-sup conditions for Chebyshev spectral approximation of the Stokes problem. Zbl 0666.76055Bernardi, Christine; Canuto, Claudio; Maday, Yvon 63 1988 A posteriori analysis of the finite element discretization of some parabolic equations. Zbl 1072.65124Bergam, A.; Bernardi, C.; Mghazli, Z. 58 2005 Variational discretization of elliptic boundary value problems. (Discrétisations variationnelles de problèmes aux limites elliptiques.) Zbl 1063.65119Bernardi, Christine; Maday, Yvon; Rapetti, Francesca 53 2004 Polynomial interpolation results in Sobolev spaces. Zbl 0767.41001Bernardi, Christine; Maday, Yvon 48 1992 A priori and a posteriori analysis of finite volume discretizations of Darcy’s equations. Zbl 1050.76035Achdou, Y.; Bernardi, C.; Coquel, F. 48 2003 Spectral methods for axisymmetric domains. Numerical algorithms and tests due to Mejdi Azaïez. Zbl 0929.35001Bernardi, Christine; Dauge, Monique; Maday, Yvon 43 1999 Uniform inf-sup conditions for the spectral discretization of the Stokes problem. Zbl 0944.76058Bernardi, C.; Maday, Y. 41 1999 Coupling the Navier-Stokes equation with the heat equation: The model and its approximation by finite elements. (Couplage des équations de Navier-Stokes et de la chaleur: Le modèle et son approximation par éléments finis.) Zbl 0839.76016Bernardi, Christine; Métivet, Brigitte; Pernaud-Thomas, Bernadette 39 1995 Basics and some applications of the mortar element method. Zbl 1177.65178Bernardi, Christine; Maday, Yvon; Rapetti, Francesca 36 2005 Weighted Clément operator and application to the finite element discretization of the axisymmetric Stokes problem. Zbl 1107.65103Belhachmi, Zakaria; Bernardi, Christine; Deparis, Simone 35 2006 Mortar finite element discretization of a model coupling Darcy and Stokes equations. Zbl 1138.76044Bernardi, Christine; Chacón Rebollo, Tomás; Hecht, Frédéric; Mghazli, Zoubida 35 2008 Properties of some weighted Sobolev spaces and application to spectral approximations. Zbl 0675.65114Bernardi, Christine; Maday, Yvon 32 1989 Coupling Darcy and Stokes equations for porous media with cracks. Zbl 1079.76041Bernardi, Christine; Hecht, Frédéric; Pironneau, Olivier 30 2005 Coupling finite element and spectral methods: First results. Zbl 0685.65098Bernardi, Christine; Debit, Naïma; Maday, Yvon 30 1990 A posteriori error analysis of the fully discretized time-dependent Stokes equations. Zbl 1079.76042Bernardi, Christine; Verfürth, Rüdiger 29 2004 Spectral discretization of the vorticity, velocity, and pressure formulation of the Stokes problem. Zbl 1117.65159Bernardi, Christine; Chorfi, Nejmeddine 28 2006 Spectral, spectral element and mortar element methods. Zbl 0991.65124Bernardi, Christine; Maday, Yvon 25 2001 A conforming finite element method for the time-dependent Navier-Stokes equations. Zbl 0578.65122Bernardi, Christine; Raugel, Geneviève 24 1985 Mixed spectral element approximation of the Navier-Stokes equations in the stream-function and vorticity formulation. Zbl 0753.76130Bernardi, Christine; Girault, Vivette; Maday, Yvon 23 1992 Mixed finite element method for the Stokes and Navier-Stokes equations in a nonconvex polxgon. (Méthodes d’éléments finis mixtes pour les équations de Stokes et de Navier-Stokes dans un polygone non convexe.) Zbl 0475.76035Bernardi, C.; Raugel, G. 21 1981 Some spectral approximations of two-dimensional fourth-order problems. Zbl 0754.65088Bernardi, Christine; Coppoletta, Giuseppe; Maday, Yvon 21 1992 Error indicators for the mortar finite element discretization of the Laplace equation. Zbl 1012.65108Bernardi, Christine; Hecht, Frédéric 21 2002 On the shallow water equations at low Reynolds number. Zbl 0723.76033Bernardi, Christine; Pironneau, Olivier 21 1991 Spectral element discretizations of the Poisson equation with mixed boundary conditions. Zbl 1004.65119Bernardi, C.; Maday, Y. 20 2001 Time and space adaptivity for the second-order wave equation. Zbl 1070.65083Bernardi, Christine; Süli, Endre 19 2005 Polynomial approximation of some singular functions. Zbl 0701.41009Bernardi, Christine; Maday, Yvon 19 1991 A collocation method over staggered grids for the Stokes problem. Zbl 0665.76037Bernardi, Christine; Maday, Yvon 19 1988 Spectral element discretization of the Maxwell equations. Zbl 0932.65110Ben Belgacem, F.; Bernardi, C. 16 1999 A finite element discretization of the three-dimensional Navier-Stokes equations with mixed boundary conditions. Zbl 1422.76124Bernardi, Christine; Hecht, Frédéric; Verfürth, Rüdiger 15 2009 Spectral discretization of Darcy’s equations coupled with the heat equation. Zbl 1433.76121Bernardi, Christine; Maarouf, Sarra; Yakoubi, Driss 14 2016 Spectral methods applied to porous media equations. Zbl 0838.76055Azaïez, M.; Bernardi, C.; Grundmann, M. 14 1994 Discretization of an unsteady flow through a porous solid modeled by Darcy’s equations. Zbl 1157.76023Bernardi, Christine; Girault, Vivette; Rajagopal, Kumbakonam R. 14 2008 A new finite-element discretization of the Stokes problem coupled with the Darcy equations. Zbl 1423.76213Bernardi, Christine; Hecht, Frédéric; Nouri, Fatma Zohra 13 2010 A model for two coupled turbulent fluids. I: Analysis of the system. Zbl 1034.35106Bernardi, C.; Chacón Rebollo, T.; Lewandowski, R.; Murat, F. 13 2002 Spectral approximation of the periodic nonperiodic Navier-Stokes equations. Zbl 0583.65085Bernardi, Christine; Maday, Yvon; Métivet, Brigitte 13 1987 A model for two coupled turbulent fluids. II: Numerical analysis of a spectral discretization. Zbl 1129.76327Bernardi, C.; Chacón Rebollo, T.; Lewandowski, R.; Murat, F. 13 2003 Convergence of a finite element discretization of the Navier-Stokes equations in vorticity and stream function formulation. Zbl 0956.76040Amara, Mohamed; Bernardi, Christine 13 1999 Inf-sup conditions for the mortar spectral element discretization of the Stokes problem. Zbl 0955.65088Ben Belgacem, F.; Bernardi, C.; Chorfi, N.; Maday, Y. 13 2000 Mortar finite element discretization for the flow in a nonhomogeneous porous medium. Zbl 1173.76331Bernardi, Christine; Hecht, Frédéric; Mghazli, Zoubida 12 2007 An error indicator for mortar element solutions to the Stokes problem. Zbl 0998.65113Bernardi, Christine; Fiétier, Nicolas; Owens, Robert G. 12 2001 A posteriori analysis of a penalty method and application to the Stokes problem. Zbl 1050.65099Bernardi, C.; Girault, V.; Hecht, F. 12 2003 Trace liftings which preserve polynomials. (Relèvements de traces préservant les polynômes.) Zbl 0755.65103Bernardi, Christine; Dauge, Monique; Maday, Yvon 11 1992 A model for two coupled turbulent fluids. III: Numerical approximation by finite elements. Zbl 1129.76326Bernardi, C.; Chacón Rebollo, T.; Gómez Mármol, M.; Lewandowski, R.; Murat, F. 11 2004 Resolution of fourth-order problems by the mortar element method. Zbl 0824.65111Belhachmi, Zakaria; Bernardi, Christine 10 1994 Calcul de la pression dans la résolution spectrale du problème de Stokes. (Computation of the pressure in the spectral approximation of the Stokes problem). Zbl 0642.76037Bernardi, C.; Maday, Y.; Métivet, B. 10 1987 Spectral discretization of the vorticity, velocity and pressure formulation of the Navier-Stokes equations. Zbl 1138.76052Azaïez, Mejdi; Bernardi, Christine; Chorfi, Nejmeddine 10 2006 A density result for Maxwell’s equations. (Un résultat de densité pour les équations de Maxwell.) Zbl 0880.35115Ben Belgacem, Faker; Bernardi, Christine; Costabel, Martin; Dauge, Monique 10 1997 Spectral methods for the approximation of fourth-order problems: Application to the Stokes and Navier-Stokes equations. Zbl 0668.76038Bernardi, Christine; Maday, Yvon 9 1988 Spectral element discretization of the circular driven cavity. II: The bilaplacian equation. Zbl 0988.65110Belhachmi, Z.; Bernardi, C.; Karageorghis, A. 9 2001 Finite element methods for Darcy’s problem coupled with the heat equation. Zbl 1393.35159Bernardi, Christine; Dib, Séréna; Girault, Vivette; Hecht, Frédéric; Murat, François; Sayah, Toni 9 2018 Noncorming matching conditions for coupling spectral and finite element methods. Zbl 0684.65099Bernardi, Christine; Maday, Yvon; Sacchi Landriani, Giovanni 9 1989 Non-conforming spectral element-finite element approximations for partial differential equations. Zbl 0697.65080Bègue, C.; Bernardi, C.; Debit, N.; Maday, Y.; Karniadakis, G. E.; Mavriplis, C.; Patera, A. T. 9 1989 Relèvement polynômial de traces et applications. (Polynomial lifting of traces and applications). Zbl 0707.65077Bernardi, Christine; Maday, Yvon 9 1990 Spectral discretization of Darcy’s equations with pressure dependent porosity. Zbl 1342.76090Azaïez, Mejdi; Ben Belgacem, Faker; Bernardi, Christine; Chorfi, Nejmeddine 9 2010 Adaptive finite volume or finite element discretization of Darcy’s equations with variable permeability. (Un schéma de volumes ou éléments finis adaptatif pour les équations de Darcy à perméabilité variable.) Zbl 0996.65123Achdou, Yves; Bernardi, Christine 9 2001 Continuity properties of the inf-sup constant for the divergence. Zbl 1339.35230Bernardi, Christine; Costabel, Martin; Dauge, Monique; Girault, Vivette 9 2016 A posteriori error analysis for two non-overlapping domain decomposition techniques. Zbl 1166.65053Bernardi, C.; Chacón Rebollo, T.; Chacón Vera, E.; Coronil, D. Franco 8 2009 Error indicators in the \(h-N\) version of spectral elements. (Indicateurs d’erreur en \(h-N\) version des éléments spectraux.) Zbl 0843.65077Bernardi, Christine 8 1996 Un problème variationnel abstrait. Application à une méthode de collocation pour les équations de Stokes. (An abstract variational problem. Application to a collocation method for the Stokes equations). Zbl 0612.49004Bernardi, Christine; Canuto, Claudio; Maday, Yvon 8 1986 Sensitivity of Darcy’s law to discontinuities. Zbl 1040.35067Bernardi, C.; Pironneau, O. 8 2003 Error indicators for the heat equation. (Indicateurs d’erreur pour l’équation de la chaleur.) Zbl 0959.65106Bernardi, Christine; Métivet, Brigitte 8 2000 Finite element discretization of the Stokes and Navier-Stokes equations with boundary conditions on the pressure. Zbl 1325.35136Bernardi, Christine; Chacón Rebollo, Tomás; Yakoubi, Driss 8 2015 A posteriori analysis of iterative algorithms for a nonlinear problem. Zbl 1331.65152Bernardi, Christine; Dakroub, Jad; Mansour, Gihane; Sayah, Toni 8 2015 On the unilateral contact between membranes. I: Finite element discretization and mixed reformulation. Zbl 1162.74031Ben Belgacem, F.; Bernardi, C.; Blouza, A.; Vohralík, M. 7 2009 Automatic insertion of a turbulence model in the finite element discretization of the Navier-Stokes equations. Zbl 1169.76031Bernardi, Christine; Chacón Rebollo, Tomás; Hecht, Frédéric; Lewandowski, Roger 7 2009 A finite element discretization of the contact between two membranes. Zbl 1157.74036Ben Belgacem, Faker; Bernardi, Christine; Blouza, Adel; Vohralík, Martin 7 2009 Finite element mesh refinement by the mortar method. (Raffinement de maillage en éléments finis par la méthode des joints.) Zbl 0830.65106Bernardi, Christine; Maday, Yvon 7 1995 A posteriori analysis of a space and time discretization of a nonlinear model for the flow in partially saturated porous media. Zbl 1353.76050Bernardi, Christine; El Alaoui, Linda; Mghazli, Zoubida 7 2014 Spectral approximations of the Stokes equations with boundary conditions on the pressure. Zbl 0727.76040Bernardi, Christine; Canuto, Claudio; Maday, Yvon 7 1991 A truncated Fourier/finite element discretization of the Stokes equations in an axisymmetric domain. Zbl 1134.76376Belhachmi, Z.; Bernardi, C.; Deparis, S.; Hecht, F. 7 2006 On the unilateral contact between membranes. II: A posteriori analysis and numerical experiments. Zbl 1451.74176Ben Belgacem, Faker; Bernardi, Christine; Blouza, Adel; Vohralík, Martin 7 2012 Spectral discretization of the Navier-Stokes equations coupled with the heat equation. Zbl 1325.35134Agroum, Rahma; Aouadi, Saloua Mani; Bernardi, Christine; Satouri, Jamil 7 2015 A posteriori error analysis of the time-dependent Stokes equations with mixed boundary conditions. Zbl 1310.65106Bernardi, Christine; Sayah, Toni 7 2015 Error indicators for the mortar finite element discretization of a parabolic problem. Zbl 1035.65102Bergam, A.; Bernardi, C.; Hecht, F.; Mghazli, Z. 6 2003 Interpolation of nullspaces for polynomial approximation of divergence- free functions in a cube. Zbl 0830.46015Bernardi, Christine; Dauge, Monique; Maday, Yvon 6 1995 Spectral approximation of a Schrödinger type equation. Zbl 0791.35026Bernardi, Christine; Pelissier, Marie-Claude 6 1994 A posteriori error analysis of the time dependent Navier-Stokes equations with mixed boundary conditions. Zbl 1327.65183Bernardi, Christine; Sayah, Toni 6 2015 Compatibility of traces on the edges and corners of a polyhedron. (Compatibilité de traces aux arêtes et coins d’un polyèdre.) Zbl 0976.52008Bernardi, Christine; Dauge, Monique; Maday, Yvon 5 2000 Approximation results for spectral methods with domain decomposition. Zbl 0686.65081Bernardi, Christine; Maday, Yvon 5 1989 Numerical approximation of a periodic linear parabolic problem. Zbl 0493.65041Bernardi, Christine 5 1982 Dirichlet boundary control for a parabolic equation with a final observation. I: A space-time mixed formulation and penalization. Zbl 1217.49005Ben Belgacem, Faker; Bernardi, Christine; Fekih, Henda El 5 2011 Approximation numérique de certaines équations paraboliques non linéaires. Zbl 0548.65071Bernardi, C.; Raugel, G. 5 1984 A posteriori analysis of a finite element discretization of a Naghdi shell model. Zbl 1329.74268Bernardi, Christine; Hecht, Frédéric; Le Dret, Hervé; Blouza, Adel 5 2013 Mortar spectral element discretization of the Laplace and Darcy equations with discontinuous coefficients. Zbl 1145.65094Belhachmi, Zakaria; Bernardi, Christine; Karageorghis, Andreas 5 2007 A posteriori analysis of iterative algorithms for Navier-Stokes problem. Zbl 1457.65179Bernardi, Christine; Dakroub, Jad; Mansour, Gihane; Sayah, Toni 5 2016 Mortar spectral element discretization of the Stokes problem in axisymmetric domains. Zbl 1299.76049Aouadi, Saloua Mani; Bernardi, Christine; Satouri, Jamil 5 2014 The lifting of polynomial traces revisited. Zbl 1227.46026Bernardi, Christine; Dauge, Monique; Maday, Yvon 4 2010 Mortar spectral element methods for elliptic equations with discontinuous coefficients. Zbl 1027.65156Bernardi, Christine; Chorfi, Nejmeddine 4 2002 A FETI method with a mesh independent condition number for the iteration matrix. Zbl 1186.65147Bernardi, C.; Chacón Rebollo, T.; Chacón Vera, E. 4 2008 Finite element approximation of viscous flows with varying density. Zbl 0755.76052Bernardi, Christine; Laval, Frédéric; Métivet, Brigitte; Pernaud- Thomas, Bernadette 4 1992 Spectral discretization of the time-dependent Navier-Stokes problem coupled with the heat equation. Zbl 1410.76315Agroum, Rahma; Bernardi, Christine; Satouri, Jamil 4 2015 A mixed method for the time-dependent Navier-Stokes problem. Zbl 0652.76018Bernardi, Christine; Godlewski, Edwige; Raugel, Geneviève 4 1987 Finite element methods for Darcy’s problem coupled with the heat equation. Zbl 1393.35159Bernardi, Christine; Dib, Séréna; Girault, Vivette; Hecht, Frédéric; Murat, François; Sayah, Toni 9 2018 A posteriori error analysis of the fully discretized time-dependent coupled Darcy and Stokes equations. Zbl 1419.65053Bernardi, Christine; Orfi, Ajmia Younes 4 2018 Convergence analysis of two numerical schemes applied to a nonlinear elliptic problem. Zbl 1398.65288Bernardi, Christine; Dakroub, Jad; Mansour, Gihane; Rafei, Farah; Sayah, Toni 1 2017 Spectral discretization of Darcy’s equations coupled with the heat equation. Zbl 1433.76121Bernardi, Christine; Maarouf, Sarra; Yakoubi, Driss 14 2016 Continuity properties of the inf-sup constant for the divergence. Zbl 1339.35230Bernardi, Christine; Costabel, Martin; Dauge, Monique; Girault, Vivette 9 2016 A posteriori analysis of iterative algorithms for Navier-Stokes problem. Zbl 1457.65179Bernardi, Christine; Dakroub, Jad; Mansour, Gihane; Sayah, Toni 5 2016 A priori error analysis of the fully discretized time-dependent coupled Darcy and Stokes equations. Zbl 1383.76331Bernardi, Christine; Orfi, Ajmia Younes 3 2016 Mortar finite element discretization of the time dependent nonlinear Darcy’s equations. Zbl 1457.65087Amoura, Karima; Bernardi, Christine; Saadi, Samira 2 2016 Spectral discretization of an unsteady flow through a porous solid. Zbl 06793311Bernardi, Christine; Maarouf, Sarra; Yakoubi, Driss 1 2016 Spectral discretization of a model for organic pollution in waters. Zbl 1353.91030Bernardi, Christine; Yakoubi, Driss 1 2016 Finite element discretization of the Stokes and Navier-Stokes equations with boundary conditions on the pressure. Zbl 1325.35136Bernardi, Christine; Chacón Rebollo, Tomás; Yakoubi, Driss 8 2015 A posteriori analysis of iterative algorithms for a nonlinear problem. Zbl 1331.65152Bernardi, Christine; Dakroub, Jad; Mansour, Gihane; Sayah, Toni 8 2015 Spectral discretization of the Navier-Stokes equations coupled with the heat equation. Zbl 1325.35134Agroum, Rahma; Aouadi, Saloua Mani; Bernardi, Christine; Satouri, Jamil 7 2015 A posteriori error analysis of the time-dependent Stokes equations with mixed boundary conditions. Zbl 1310.65106Bernardi, Christine; Sayah, Toni 7 2015 A posteriori error analysis of the time dependent Navier-Stokes equations with mixed boundary conditions. Zbl 1327.65183Bernardi, Christine; Sayah, Toni 6 2015 Spectral discretization of the time-dependent Navier-Stokes problem coupled with the heat equation. Zbl 1410.76315Agroum, Rahma; Bernardi, Christine; Satouri, Jamil 4 2015 Finite element methods for the temperature in composite media with contact resistance. Zbl 1323.80004Ben Belgacem, Faker; Bernardi, Christine; Jelassi, Faten; Mint Brahim, Maimouna 4 2015 Finite element discretization of the time dependent axisymmetric Darcy problem. Zbl 1330.76063Bernardi, Christine; Orfi, Ajmia Younes 4 2015 A posteriori analysis of a space and time discretization of a nonlinear model for the flow in partially saturated porous media. Zbl 1353.76050Bernardi, Christine; El Alaoui, Linda; Mghazli, Zoubida 7 2014 Mortar spectral element discretization of the Stokes problem in axisymmetric domains. Zbl 1299.76049Aouadi, Saloua Mani; Bernardi, Christine; Satouri, Jamil 5 2014 Finite element discretization of a nonlinear thermoelastic beam model with penalized unilateral contact. Zbl 1420.74010Bernardi, Christine; Copetti, Maria Inês M. 2 2014 On Friedrichs constant and Horgan-Payne angle for LBB condition. Zbl 1360.35174Dauge, Monique; Bernardi, Christine; Costabel, Martin; Girault, Vivette 2 2014 Stabilized finite elements for a reaction-dispersion saddle-point problem with nonconstant coefficients. Zbl 1311.65142Ben Belgacem, Faker; Bernardi, Christine; Hecht, Frédéric; Salmon, Stéphanie 1 2014 A posteriori analysis of a finite element discretization of a Naghdi shell model. Zbl 1329.74268Bernardi, Christine; Hecht, Frédéric; Le Dret, Hervé; Blouza, Adel 5 2013 Automatic simplification of darcy’s equations with pressure dependent permeability. Zbl 1311.76128Ahusborde, Etienne; Azaïez, Mejdi; Ben Belgacem, Faker; Bernardi, Christine 3 2013 On the unilateral contact between membranes. II: A posteriori analysis and numerical experiments. Zbl 1451.74176Ben Belgacem, Faker; Bernardi, Christine; Blouza, Adel; Vohralík, Martin 7 2012 A posteriori analysis of a positive streamwise invariant discretization of a convection-diffusion equation. Zbl 1256.65096Bernardi, Christine; Chacón Rebollo, Tomás; Restelli, Marco 1 2012 An incompressible fluid in a weakly deformable shell. I: Analysis of the model. Zbl 1290.74013Bernardi, Christine; Blouza, Adel; Hecht, Frédéric 1 2012 Dirichlet boundary control for a parabolic equation with a final observation. I: A space-time mixed formulation and penalization. Zbl 1217.49005Ben Belgacem, Faker; Bernardi, Christine; Fekih, Henda El 5 2011 On the obstacle problem for a Naghdi shell. Zbl 1273.74350Ben Belgacem, Faker; Bernardi, Christine; Blouza, Adel; Taallah, Frekh 3 2011 A posteriori error analysis of the method of characteristics. Zbl 1228.65181Bernardi, Christine; Hecht, Frédéric; Verfürth, Rüdiger 2 2011 A penalty algorithm for the spectral element discretization of the Stokes problem. Zbl 1267.76023Bernardi, Christine; Blouza, Adel; Chorfi, Nejmeddine; Kharrat, Nizar 2 2011 A new finite-element discretization of the Stokes problem coupled with the Darcy equations. Zbl 1423.76213Bernardi, Christine; Hecht, Frédéric; Nouri, Fatma Zohra 13 2010 Spectral discretization of Darcy’s equations with pressure dependent porosity. Zbl 1342.76090Azaïez, Mejdi; Ben Belgacem, Faker; Bernardi, Christine; Chorfi, Nejmeddine 9 2010 The lifting of polynomial traces revisited. Zbl 1227.46026Bernardi, Christine; Dauge, Monique; Maday, Yvon 4 2010 A finite element discretization of the three-dimensional Navier-Stokes equations with mixed boundary conditions. Zbl 1422.76124Bernardi, Christine; Hecht, Frédéric; Verfürth, Rüdiger 15 2009 A posteriori error analysis for two non-overlapping domain decomposition techniques. Zbl 1166.65053Bernardi, C.; Chacón Rebollo, T.; Chacón Vera, E.; Coronil, D. Franco 8 2009 On the unilateral contact between membranes. I: Finite element discretization and mixed reformulation. Zbl 1162.74031Ben Belgacem, F.; Bernardi, C.; Blouza, A.; Vohralík, M. 7 2009 Automatic insertion of a turbulence model in the finite element discretization of the Navier-Stokes equations. Zbl 1169.76031Bernardi, Christine; Chacón Rebollo, Tomás; Hecht, Frédéric; Lewandowski, Roger 7 2009 A finite element discretization of the contact between two membranes. Zbl 1157.74036Ben Belgacem, Faker; Bernardi, Christine; Blouza, Adel; Vohralík, Martin 7 2009 Computing Gowdy spacetimes via spectral evolution in future and past directions. Zbl 1158.83301Amorim, Paulo; Bernardi, Christine; LeFloch, Philippe G. 3 2009 Mortar finite element discretization of a model coupling Darcy and Stokes equations. Zbl 1138.76044Bernardi, Christine; Chacón Rebollo, Tomás; Hecht, Frédéric; Mghazli, Zoubida 35 2008 Discretization of an unsteady flow through a porous solid modeled by Darcy’s equations. Zbl 1157.76023Bernardi, Christine; Girault, Vivette; Rajagopal, Kumbakonam R. 14 2008 A FETI method with a mesh independent condition number for the iteration matrix. Zbl 1186.65147Bernardi, C.; Chacón Rebollo, T.; Chacón Vera, E. 4 2008 The mortar spectral element method in domains of operators. II: The curl operator and the vector potential problem. Zbl 1139.65073Azaïez, M.; Ben Belgacem, F.; Bernardi, C.; El Rhabi, M. 1 2008 Mortar finite element discretization for the flow in a nonhomogeneous porous medium. Zbl 1173.76331Bernardi, Christine; Hecht, Frédéric; Mghazli, Zoubida 12 2007 Mortar spectral element discretization of the Laplace and Darcy equations with discontinuous coefficients. Zbl 1145.65094Belhachmi, Zakaria; Bernardi, Christine; Karageorghis, Andreas 5 2007 Some further approximation properties of Nédélec finite elements, aapplication to a posteriori analysis. (Quelques propriétés d’approximation des éléments finis de nédélec, application à l’analyse a posteriori.) Zbl 1114.65139Bernardi, Christine; Hecht, Frédéric 4 2007 Spectral discretization of a Naghdi shell model. Zbl 1154.74048Bernardi, Christine; Blouza, Adel 2 2007 A trace result for nonconforming Crouzeix-Raviart finite elements, application to the discretization of Darcy’s equations. (Un résultat de trace pour les éléments finis de Crouzeix-Raviart, application à la discrétisation des équations de Darcy.) Zbl 1110.65107Bernardi, Christine; Girault, Vivette 1 2007 Weighted Clément operator and application to the finite element discretization of the axisymmetric Stokes problem. Zbl 1107.65103Belhachmi, Zakaria; Bernardi, Christine; Deparis, Simone 35 2006 Spectral discretization of the vorticity, velocity, and pressure formulation of the Stokes problem. Zbl 1117.65159Bernardi, Christine; Chorfi, Nejmeddine 28 2006 Spectral discretization of the vorticity, velocity and pressure formulation of the Navier-Stokes equations. Zbl 1138.76052Azaïez, Mejdi; Bernardi, Christine; Chorfi, Nejmeddine 10 2006 A truncated Fourier/finite element discretization of the Stokes equations in an axisymmetric domain. Zbl 1134.76376Belhachmi, Z.; Bernardi, C.; Deparis, S.; Hecht, F. 7 2006 An efficient discretization of the Navier-Stokes equations in an axisymmetric domain. I: The discrete problem and its numerical analysis. Zbl 1101.76031Belhachmi, Z.; Bernardi, C.; Deparis, S.; Hecht, F. 3 2006 Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem. Zbl 1109.76044Amoura, Karima; Bernardi, Christine; Chorfi, Nejmeddine 3 2006 The mortar spectral element method in domains of operators. I: The divergence operator and Darcy’s equations. Zbl 1094.65116Azaïez, M.; Ben Belgacem, F.; Bernardi, C. 1 2006 A posteriori analysis of the finite element discretization of some parabolic equations. Zbl 1072.65124Bergam, A.; Bernardi, C.; Mghazli, Z. 58 2005 Basics and some applications of the mortar element method. Zbl 1177.65178Bernardi, Christine; Maday, Yvon; Rapetti, Francesca 36 2005 Coupling Darcy and Stokes equations for porous media with cracks. Zbl 1079.76041Bernardi, Christine; Hecht, Frédéric; Pironneau, Olivier 30 2005 Time and space adaptivity for the second-order wave equation. Zbl 1070.65083Bernardi, Christine; Süli, Endre 19 2005 Regularized finite element discretizations of a grade-two fluid model. Zbl 1072.76036Amara, M.; Bernardi, C.; Girault, V.; Hecht, F. 1 2005 Numerical analysis of a model for an axisymmetric guide for electromagnetic waves. I: The continuous problem and its Fourier expansion. Zbl 1125.35099Ben Belgacem, Faker; Bernardi, Christine; Rapetti, Francesca 1 2005 Variational discretization of elliptic boundary value problems. (Discrétisations variationnelles de problèmes aux limites elliptiques.) Zbl 1063.65119Bernardi, Christine; Maday, Yvon; Rapetti, Francesca 53 2004 A posteriori error analysis of the fully discretized time-dependent Stokes equations. Zbl 1079.76042Bernardi, Christine; Verfürth, Rüdiger 29 2004 A model for two coupled turbulent fluids. III: Numerical approximation by finite elements. Zbl 1129.76326Bernardi, C.; Chacón Rebollo, T.; Gómez Mármol, M.; Lewandowski, R.; Murat, F. 11 2004 A new formulation of the Stokes problem in a cylinder, and its spectral discretization. Zbl 1079.76055Abdellatif, Nehla; Bernardi, Christine 3 2004 Spectral element discretization of the circular driven cavity. IV: the Navier-Stokes equations. Zbl 1084.65121Belhachmi, Zakaria; Bernardi, Christine; Karageorghis, Andreas 3 2004 A priori and a posteriori analysis of finite volume discretizations of Darcy’s equations. Zbl 1050.76035Achdou, Y.; Bernardi, C.; Coquel, F. 48 2003 A model for two coupled turbulent fluids. II: Numerical analysis of a spectral discretization. Zbl 1129.76327Bernardi, C.; Chacón Rebollo, T.; Lewandowski, R.; Murat, F. 13 2003 A posteriori analysis of a penalty method and application to the Stokes problem. Zbl 1050.65099Bernardi, C.; Girault, V.; Hecht, F. 12 2003 Sensitivity of Darcy’s law to discontinuities. Zbl 1040.35067Bernardi, C.; Pironneau, O. 8 2003 Error indicators for the mortar finite element discretization of a parabolic problem. Zbl 1035.65102Bergam, A.; Bernardi, C.; Hecht, F.; Mghazli, Z. 6 2003 Spectral element discretization of the circular driven cavity. Part III: The Stokes equations in primitive variables. Zbl 1031.65135Belhachmi, Z.; Bernardi, Christine; Karageorghis, Andreas 1 2003 Choice of the penalty parameter for the finite element discretization of Navier-Stokes equations. (Choix du paramètre de pénalisation pour la discrétisation par éléments finis des équations de Navier-Stokes.) Zbl 1140.76361Bernardi, Christine; Girault, Vivette; Hecht, Frédéric 1 2003 Error indicators for the mortar finite element discretization of the Laplace equation. Zbl 1012.65108Bernardi, Christine; Hecht, Frédéric 21 2002 A model for two coupled turbulent fluids. I: Analysis of the system. Zbl 1034.35106Bernardi, C.; Chacón Rebollo, T.; Lewandowski, R.; Murat, F. 13 2002 Mortar spectral element methods for elliptic equations with discontinuous coefficients. Zbl 1027.65156Bernardi, Christine; Chorfi, Nejmeddine 4 2002 Derivative with respect to discontinuities in the porosity. Zbl 1013.76085Bernardi, Christine; Pironneau, Olivier 3 2002 Spectral, spectral element and mortar element methods. Zbl 0991.65124Bernardi, Christine; Maday, Yvon 25 2001 Spectral element discretizations of the Poisson equation with mixed boundary conditions. Zbl 1004.65119Bernardi, C.; Maday, Y. 20 2001 An error indicator for mortar element solutions to the Stokes problem. Zbl 0998.65113Bernardi, Christine; Fiétier, Nicolas; Owens, Robert G. 12 2001 Spectral element discretization of the circular driven cavity. II: The bilaplacian equation. Zbl 0988.65110Belhachmi, Z.; Bernardi, C.; Karageorghis, A. 9 2001 Adaptive finite volume or finite element discretization of Darcy’s equations with variable permeability. (Un schéma de volumes ou éléments finis adaptatif pour les équations de Darcy à perméabilité variable.) Zbl 0996.65123Achdou, Yves; Bernardi, Christine 9 2001 A finite element problem issued from fictious domain techniques. Zbl 1002.65127Bernardi, C.; Girault, V.; Hecht, F.; Kawarada, H.; Pironneau, O. 3 2001 Adaptive finite element methods for elliptic equations with non-smooth coefficients. Zbl 0962.65096Bernardi, C.; Verfürth, R. 85 2000 Inf-sup conditions for the mortar spectral element discretization of the Stokes problem. Zbl 0955.65088Ben Belgacem, F.; Bernardi, C.; Chorfi, N.; Maday, Y. 13 2000 Error indicators for the heat equation. (Indicateurs d’erreur pour l’équation de la chaleur.) Zbl 0959.65106Bernardi, Christine; Métivet, Brigitte 8 2000 Compatibility of traces on the edges and corners of a polyhedron. (Compatibilité de traces aux arêtes et coins d’un polyèdre.) Zbl 0976.52008Bernardi, Christine; Dauge, Monique; Maday, Yvon 5 2000 Mesh adaptivity in finite elements using the mortar method. Zbl 0954.65081Bernardi, Christine; Maday, Yvon 4 2000 More pressure in the finite element discretization of the Stokes problem. Zbl 0992.76051Bernardi, Christine; Hecht, Frédéric 2 2000 A model for two coupled turbulent fluids. Zbl 1009.76044Bernardi, C.; Chacón Rebollo, T.; Lewandowski, R.; Murat, F. 1 2000 Spectral methods for axisymmetric domains. Numerical algorithms and tests due to Mejdi Azaïez. Zbl 0929.35001Bernardi, Christine; Dauge, Monique; Maday, Yvon 43 1999 Uniform inf-sup conditions for the spectral discretization of the Stokes problem. Zbl 0944.76058Bernardi, C.; Maday, Y. 41 1999 Spectral element discretization of the Maxwell equations. Zbl 0932.65110Ben Belgacem, F.; Bernardi, C. 16 1999 Convergence of a finite element discretization of the Navier-Stokes equations in vorticity and stream function formulation. Zbl 0956.76040Amara, Mohamed; Bernardi, Christine 13 1999 An improved inf-sup condition for the spectral discretization of the Stokes problem in a cylinder. Zbl 0934.76066Bernardi, Christine 1 1999 Existence of a solution for a model of two coupled turbulent fluids. (Existence d’une solution pour un modèle de deux fluides turbulents couplés.) Zbl 0930.35131Bernardi, Christine; Chacon, Tomas; Lewandowski, Roger; Murat, François 1 1999 Spectral element discretization of the circular driven cavity. I: The Laplace equation. Zbl 0932.65118Bernardi, C.; Karageorghis, A. 1 1999 Vector potentials in three-dimensional non-smooth domains. Zbl 0914.35094Amrouche, C.; Bernardi, C.; Dauge, M.; Girault, V. 380 1998 ...and 49 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,449 Authors 68 Bernardi, Christine 37 Maday, Yvon 34 Gatica, Gabriel N. 28 Nicaise, Serge 26 Ciarlet, Patrick jun. 25 Chacón Rebollo, Tomás 25 Wohlmuth, Barbara I. 23 Ruiz-Baier, Ricardo 22 Girault, Vivette 22 Guo, Ben-Yu 21 Ben Belgacem, Faker 21 Hecht, Frédéric 21 Quarteroni, Alfio M. 20 Chorfi, Nejmeddine 20 Oyarzúa, Ricardo 19 Rodríguez, Rodolfo 19 Vohralík, Martin 17 Duan, Huoyuan 17 Rapetti, Francesca 16 Amrouche, Chérif 15 Gervasio, Paola 14 Azaïez, Mejdi 14 Buffa, Annalisa 14 Chen, Jinru 14 Xu, Chuanju 13 Hiptmair, Ralf 13 Sayah, Toni 13 Yakoubi, Driss 12 Abdelwahed, Mohamed 12 Bertoluzza, Silvia 12 Li, Huiyuan 12 Mora, David 12 Neilan, Michael 12 Perugia, Ilaria 12 Shen, Jie 12 Zhang, Zhimin 11 Hild, Patrick 11 Lamichhane, Bishnu Prasad 11 Stephan, Ernst Peter 11 Zhang, Shangyou 11 Zou, Jun 10 Anaya, Verónica 10 Belhachmi, Zakaria 10 Dauge, Monique 10 Guermond, Jean-Luc 10 Heinrichs, Wilhelm 10 Hou, Yanren 10 Karageorghis, Andreas 10 Seshaiyer, Padmanabhan 9 Ainsworth, Mark 9 Beirão da Veiga, Lourenço 9 Bermúdez, Alfredo 9 Cai, Zhiqiang 9 Colmenares, Eligio 9 Dehghan Takht Fooladi, Mehdi 9 Li, Jichun 9 Meddahi, Salim 9 Otárola, Enrique 9 Pasciak, Joseph E. 9 Pavarino, Luca Franco 9 Salgado, Abner J. 9 Sinha, Rajen Kumar 9 Yotov, Ivan 9 Zhang, Shun 8 Burman, Erik 8 Carstensen, Carsten 8 Costabel, Martin 8 Deparis, Simone 8 Ern, Alexandre 8 Gómez Mármol, Macarena 8 He, Xiaoming 8 He, Yinnian 8 Houston, Paul 8 Huang, Yunqing 8 Mao, Shipeng 8 Nochetto, Ricardo Horacio 8 Novo, Julia 8 Park, Eun-Jae 8 Pauly, Dirk 8 Rønquist, Einar M. 8 Salgado, Pilar 8 Sayas, Francisco-Javier 8 Tan, Roger C. E. 8 Venegas, Pablo 8 Xu, Xuejun 8 Yousept, Irwin 8 Zhou, Jianwei 7 Alonso Rodríguez, Ana 7 Berrone, Stefano 7 Deville, Michel O. 7 Guzmán, Johnny 7 Huang, Jianguo 7 Joly, Patrick 7 Kang, Tong 7 Laursen, Tod A. 7 Mascotto, Lorenzo 7 Melenk, Jens Markus 7 Pironneau, Olivier 7 Schötzau, Dominik 7 Slodička, Marián ...and 2,349 more Authors all top 5 Cited in 227 Serials 224 Computer Methods in Applied Mechanics and Engineering 111 Journal of Scientific Computing 105 Computers & Mathematics with Applications 102 Journal of Computational and Applied Mathematics 102 Numerische Mathematik 97 Mathematics of Computation 80 Journal of Computational Physics 80 Applied Numerical Mathematics 58 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 50 SIAM Journal on Numerical Analysis 44 Applied Mathematics and Computation 41 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 37 Comptes Rendus. Mathématique. 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