Edit Profile (opens in new tab) Girault, Vivette Compute Distance To: Compute Author ID: girault.vivette Published as: Girault, Vivette; Girault, V. External Links: MGP · Wikidata · dblp · GND · IdRef · theses.fr Documents Indexed: 123 Publications since 1967, including 4 Books Co-Authors: 70 Co-Authors with 110 Joint Publications 2,328 Co-Co-Authors all top 5 Co-Authors 12 single-authored 15 Bernardi, Christine 15 Rivière, Beatrice M. 14 Scott, Larkin Ridgway 14 Wheeler, Mary Fanett 11 Amrouche, Chérif 9 Hecht, Frédéric 7 Giroire, Jean 7 Glowinski, Roland 5 Chacón Rebollo, Tomás 5 Murat, François 5 Raviart, Pierre-Arnaud 5 Sequeira, Adélia 4 Cioranescu, Doina 4 Gómez Mármol, Macarena 4 Sayah, Toni 3 Ben Belgacem, Faker 3 Dauge, Monique 3 Jelassi, Faten 3 Nochetto, Ricardo Horacio 3 Pironneau, Olivier 3 Rajagopal, Kumbakonam Ramamani 2 Abboud, Hyam 2 Amara, Mohamed 2 Bonito, Andrea 2 Cappanera, Loïc 2 Casado-Díaz, Juan 2 Chaabane, Nabil 2 Costabel, Martin 2 Dib, Séréna 2 Kumar, Kundan 2 Li, Jizhou 2 Lions, Jacques-Louis 2 Maday, Yvon 2 Maury, Bertrand 2 Pencheva, Gergina V. 2 Sánchez Muñoz, Isabel 2 Süli, Endre E. 2 Vila, Jean-Paul 2 Wildey, Tim M. 2 Yotov, Ivan 1 Abboud, Toufic 1 Çeşmelioğlu, Ayçıl 1 Ciarlet, Patrick jun. 1 Coppoletta, Giuseppe 1 Coulet, Julien 1 Faille, Isabelle 1 Ganis, Benjamin 1 Guignard, Diane 1 Guillén González, Francisco M. 1 Guy, Nicolas 1 Halpern, Laurence 1 Joshaghani, M. S. 1 Kanschat, Guido 1 Kawarada, Hideo 1 Li, Hanyu 1 Lu, Xueying 1 Mear, Mark E. 1 Nataf, Frédéric 1 Pan, Tsorng-Whay 1 Puelz, Charles 1 Saadouni, M. 1 Salgado, Abner J. 1 Schonbek, Maria Elena 1 Schonbek, Tomas P. 1 Singh, Gurpreet 1 Sun, Shuyu 1 Tartar, Luc C. 1 Thompson, Travis B. 1 Vassilev, Danail 1 Wu, Po-Yi all top 5 Serials 11 Numerische Mathematik 9 SIAM Journal on Numerical Analysis 8 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 IMA Journal of Numerical Analysis 6 Mathematics of Computation 6 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 5 Computer Methods in Applied Mechanics and Engineering 5 Journal of Numerical Mathematics 4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Comptes Rendus de l’Académie des Sciences. Série I 3 SIAM Journal on Mathematical Analysis 3 Computational Geosciences 2 Computers & Mathematics with Applications 2 Mathematical Methods in the Applied Sciences 2 Numerical Methods for Partial Differential Equations 2 East-West Journal of Numerical Mathematics 2 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 2 Lecture Notes in Mathematics 1 Archive for Rational Mechanics and Analysis 1 International Journal of Non-Linear Mechanics 1 International Journal for Numerical Methods in Fluids 1 Journal of Computational Physics 1 Revue Roumaine de Mathématiques Pures et Appliquées 1 Calcolo 1 Czechoslovak Mathematical Journal 1 Journal of Computational and Applied Mathematics 1 Journal of the Faculty of Science. Section I A 1 Portugaliae Mathematica 1 Proceedings of the Japan Academy. Series A 1 Acta Applicandae Mathematicae 1 Applied Numerical Mathematics 1 Japan Journal of Industrial and Applied Mathematics 1 Differential and Integral Equations 1 Divulgaciones Matemáticas 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Portugaliae Mathematica. Nova Série 1 Revue Française d’Informatique et de Recherche Opérationnelle 1 Springer Series in Computational Mathematics 1 Advances in Mechanics and Mathematics 1 Nonlinear Analysis. Theory, Methods & Applications all top 5 Fields 85 Fluid mechanics (76-XX) 79 Numerical analysis (65-XX) 72 Partial differential equations (35-XX) 9 Functional analysis (46-XX) 8 Mechanics of deformable solids (74-XX) 2 Geophysics (86-XX) 1 Real functions (26-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 104 Publications have been cited 5,797 times in 4,665 Documents Cited by ▼ Year ▼ Finite element methods for Navier-Stokes equations. Theory and algorithms. (Extended version of the 1979 publ.). Zbl 0585.65077Girault, Vivette; Raviart, Pierre-Arnaud 2,026 1986 Finite element approximation of the Navier-Stokes equations. Zbl 0413.65081Girault, V.; Raviart, P.-A. 664 1979 An analysis of a mixed finite element method for the Navier-Stokes equations. Zbl 0396.65070Girault, V.; Raviart, P. A. 410 1979 Vector potentials in three-dimensional non-smooth domains. Zbl 0914.35094Amrouche, C.; Bernardi, C.; Dauge, M.; Girault, V. 388 1998 A priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems. Zbl 1010.65045Rivière, Béatrice; Wheeler, Mary F.; Girault, Vivette 188 2001 Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I. Zbl 0951.65108Rivière, Béatrice; Wheeler, Mary F.; Girault, Vivette 181 1999 Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension. Zbl 0823.35140Amrouche, Chérif; Girault, Vivette 137 1994 DG approximation of coupled Navier-Stokes and Darcy equations by Beaver-Joseph-Saffman interface condition. Zbl 1406.76082Girault, Vivette; Rivière, Béatrice 116 2009 A discontinuous Galerkin method with nonoverlapping domain decomposition for the Stokes and Navier-Stokes problems. Zbl 1057.35029Girault, Vivette; Rivière, Béatrice; Wheeler, Mary F. 94 2005 A local regularization operator for triangular and quadrilateral finite elements. Zbl 0913.65007Bernardi, C.; Girault, V. 85 1998 Dirichlet and Neumann exterior problems for the \(n\)-dimensional Laplace operator. An approach in weighted Sobolev spaces. Zbl 0878.35029Amrouche, C.; Girault, V.; Giroire, J. 74 1997 Two-grid finite element schemes for the transient Navier-Stokes problem. Zbl 1032.76032Girault, Vivette; Lions, Jacques-Louis 73 2001 Error analysis of a fictitious domain method applied to a Dirichlet problem. Zbl 0843.65076Girault, V.; Glowinski, R. 67 1995 Finite element approximation of the Navier-Stokes equations. Rev. repr. of the 1st ed. Zbl 0441.65081Girault, V.; Raviart, P.-A. 65 1981 Two-grid finite-element schemes for the steady Navier-Stokes problem in polyhedra. Zbl 0997.76043Girault, V.; Lions, J.-L. 64 2001 Weighted Sobolev spaces for Laplace’s equation in \(\mathbb{R}^ n\). Zbl 0836.35038Amrouche, C.; Girault, V.; Giroire, J. 57 1994 Weak and classical solutions of a family of second grade fluids. Zbl 0891.76005Cioranescu, D.; Girault, V. 51 1997 Numerical discretization of a Darcy-Forchheimer model. Zbl 1143.76035Girault, V.; Wheeler, M. F. 50 2008 Mortar multiscale finite element methods for Stokes-Darcy flows. Zbl 1396.76051Girault, Vivette; Vassilev, Danail; Yotov, Ivan 43 2014 A quasi-local interpolation operator preserving the discrete divergence. Zbl 1072.65014Girault, V.; Scott, L. R. 41 2003 On the existence and regularity of the solution of Stokes problem in arbitrary dimension. Zbl 0752.35047Amrouche, Chérif; Girault, Vivette 40 1991 Convergence of iterative coupling of geomechanics with flow in a fractured poroelastic medium. Zbl 1391.76650Girault, Vivette; Kumar, Kundan; Wheeler, Mary F. 38 2016 Finite-element error estimates for the MAC scheme. Zbl 0853.76037Girault, V.; Lopez, H. 35 1996 A lubrication fracture model in a poro-elastic medium. Zbl 1309.76194Girault, V.; Wheeler, M. F.; Ganis, B.; Mear, M. E. 35 2015 Incompressible finite element methods for Navier-Stokes equations with nonstandard boundary conditions in \(R^ 3\). Zbl 0666.76053Girault, V. 32 1988 Maximum-norm stability of the finite element Stokes projection. Zbl 1210.76051Girault, V.; Nochetto, R. H.; Scott, R. 31 2005 A well-posed problem for the exterior Stokes equations in two and three dimensions. Zbl 0731.35078Girault, Vivette; Sequeira, Adelia 30 1991 Time-dependent coupling of Navier–Stokes and Darcy flows. Zbl 1267.76096Cesmelioglu, Aycil; Girault, Vivette; Rivière, Béatrice 29 2013 Coupling discontinuous Galerkin and mixed finite element discretizations using mortar finite elements. Zbl 1165.65075Girault, Vivette; Sun, Shuyu; Wheeler, Mary F.; Yotov, Ivan 28 2008 A second order accuracy for a full discretized time-dependent Navier-Stokes equations by a two-grid scheme. Zbl 1407.76111Abboud, Hyam; Girault, Vivette; Sayah, Toni 28 2009 Hermite interpolation of nonsmooth functions preserving boundary conditions. Zbl 1002.65129Girault, V.; Scott, L. R. 25 2002 Analysis of a two-dimensional grade-two fluid model with a tangential boundary condition. Zbl 0961.35116Girault, V.; Scott, L. R. 25 1999 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 Mechanics and mathematics of fluids of the differential type. Zbl 1365.76001Cioranescu, D.; Girault, V.; Rajagopal, K. R. 20 2016 Pointwise decay of solutions and of higher derivatives to Navier-Stokes equations. Zbl 0986.35085Amrouche, Cherif; Girault, Vivette; Schonbek, Maria Elena; Schonbek, Tomas P. 20 2000 Theory of a finite difference method on irregular networks. Zbl 0296.65049Girault, V. 20 1974 A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations. Zbl 1085.76037Girault, Vivette; Rivière, Béatrice; Wheeler, Mary F. 19 2005 Finite elements approximation of second order linear elliptic equations in divergence form with right-hand side in \(L^1\). Zbl 1144.65072Casado-Díaz, J.; Chacón Rebollo, T.; Girault, V.; Gómez Mármol, M.; Murat, F. 18 2007 Max-norm estimates for Stokes and Navier-Stokes approximations in convex polyhedra. Zbl 1401.76087Girault, V.; Nochetto, R. H.; Scott, L. R. 18 2015 A high order term-by-term stabilization solver for incompressible flow problems. Zbl 1426.76234Chacón Rebollo, T.; Gómez Mármol, M.; Girault, V.; Sánchez Muñoz, I. 17 2013 Domain decomposition for poroelasticity and elasticity with DG jumps and mortars. Zbl 1216.35153Girault, V.; Pencheva, G.; Wheeler, M. F.; Wildey, T. 16 2011 The Stokes problem and vector potential operator in three-dimensional exterior domains: An approach in weighted Sobolev spaces. Zbl 0831.35125Girault, V. 15 1994 Discontinuous finite element methods for incompressible flows on subdomains with non-matching interfaces. Zbl 1121.76038Rivière, Béatrice; Girault, Vivette 14 2006 Inf-sup condition for the 3-D \(P_2\)-iso-\(P_1\) Taylor-Hood finite element; application to Maxwell equations. (Condition inf-sup pour l’élément fini de Taylor-Hood \(P_2\)-iso-\(P_1\), 3-D; application aux équations de Maxwell.) Zbl 1021.78009Ciarlet, Patrick jun.; Girault, Vivette 14 2002 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 Error analysis for a monolithic discretization of coupled Darcy and Stokes problems. Zbl 1302.76101Girault, V.; Kanschat, G.; Rivière, B. 14 2014 A stream-function–vorticity variational formulation for the exterior Stokes problem in weighted Sobolev spaces. Zbl 0761.35083Girault, V.; Giroire, J.; Sequeira, A. 13 1992 A fictitious-domain method with distributed multiplier for the Stokes problem. Zbl 0954.35127Girault, Vivette; Glowinski, Roland; Pan, T. W. 13 1999 Mixed formulation, approximation and decoupling algorithm for a penalized nematic liquid crystals model. Zbl 1228.35176Girault, V.; Guillén-González, F. 13 2011 The gradient, divergence, curl and Stokes operators in weighted Sobolev spaces of \(\mathbb{R}^ 3\). Zbl 0779.35088Girault, V. 12 1992 A posteriori analysis of a penalty method and application to the Stokes problem. Zbl 1050.65099Bernardi, C.; Girault, V.; Hecht, F. 12 2003 An analysis of upwind schemes for the Navier-Stokes equations. Zbl 0487.76036Girault, V.; Raviart, P.-A. 12 1982 Generalized Stokes problems. (Problèmes généralisés de Stokes.) Zbl 0790.35084Amrouche, Chérif; Girault, Vivette 10 1992 A combined finite element and marker and cell method for solving Navier-Stokes equations. Zbl 0313.65105Girault, V. 10 1976 A boundary multiplier/fictitious domain method for the steady incompressible Navier-Stokes equations. Zbl 1002.76067Girault, V.; Glowinski, R.; López, H.; Vila, J.-P. 10 2001 Continuity properties of the inf-sup constant for the divergence. Zbl 1339.35230Bernardi, Christine; Costabel, Martin; Dauge, Monique; Girault, Vivette 9 2016 Analysis of a coupled fluid-structure model with applications to hemodynamics. Zbl 1343.35184Chacón Rebollo, T.; Girault, V.; Murat, F.; Pironneau, O. 9 2016 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 fully coupled scheme using virtual element method and finite volume for poroelasticity. Zbl 1434.86001Coulet, Julien; Faille, Isabelle; Girault, Vivette; Guy, Nicolas; Nataf, Frédéric 9 2020 One time-step finite element discretization of the equation of motion of two-fluid flows. Zbl 1089.76032Girault, V.; López, H.; Maury, B. 7 2006 On a time-dependent grade-two fluid model in two dimensions. Zbl 1122.76009Girault, V.; Saadouni, M. 7 2007 A posteriori error estimates for Biot system using enriched Galerkin for flow. Zbl 1506.76075Girault, Vivette; Lu, Xueying; Wheeler, Mary F. 7 2020 \(L^p\) and \(W^{1,p}\) regularity of the solution of a steady transport equation. (Régularité dans \(L^p\) et \(W^{1,p}\) de la solution d’une équation de transport stationnaire.) Zbl 1200.35207Girault, Vivette; Tartar, Luc 7 2010 Domain decomposition for linear elasticity with DG jumps and mortars. Zbl 1227.74069Girault, Vivette; Pencheva, Gergina V.; Wheeler, Mary F.; Wildey, Tim M. 7 2009 Finite element discretization of Darcy’s equations with pressure-dependent porosity. Zbl 1271.76166Girault, Vivette; Murat, François; Salgado, Abner 7 2010 Convergence of IPDG for coupled time-dependent Navier-Stokes and Darcy equations. Zbl 1432.65145Chaabane, Nabil; Girault, Vivette; Puelz, Charles; Riviere, Beatrice 7 2017 Stability of the finite element Stokes projection in \(W^{1,\infty}\). Zbl 1049.65118Girault, Vivette; Nochetto, Ricardo H.; Scott, Ridgway 6 2004 A domain decomposition and mixed method for a linear parabolic boundary value problem. Zbl 1062.65101Girault, V.; Glowinski, R.; López, H. 6 2004 Discontinuous Galerkin methods. Zbl 1149.65323Girault, Vivette; Wheeler, Mary F. 6 2008 Strong convergence of discrete DG solutions of the heat equation. Zbl 1352.65290Girault, Vivette; Li, Jizhou; Rivière, Beatrice 6 2016 A local projection operator for quadrilateral finite elements. Zbl 0856.65128Girault, V. 5 1995 Two-grid finite element scheme for the fully discrete time-dependent Navier-Stokes problem. Zbl 1078.65083Abboud, Hyam; Girault, Vivette; Sayah, Toni 5 2005 On a time-dependent transport equation in a Lipschitz domain. Zbl 1217.35048Girault, V.; Scott, L. Ridgway 5 2010 A stream function-vorticity variational formulation for the exterior Stokes problem in weighted Sobolev spaces. (Formulation variationnelle en fonction courant-tourbillon du problème de Stokes extérieur dans des espaces de Sobolev à poids.) Zbl 0737.35064Girault, Vivette; Giroire, Jean; Sequeira, Adelia 4 1991 Weighted Sobolev spaces and Laplace’s equation in \(\mathbb{R}^ n\). I. (Espaces de Sobolev avec poids et équation de Laplace dans \(\mathbb{R}^ n\). I.) Zbl 0801.46035Amrouche, Chérif; Girault, Vivette; Giroire, Jean 4 1992 Mixed formulation of a linearized lubrication fracture model in a poro-elastic medium. Zbl 1416.35263Girault, Vivette; Wheeler, Mary F.; Kumar, Kundan; Singh, Gurpreet 4 2019 Finite element discretizations of a two-dimensional grade-two fluid model. Zbl 1032.76033Girault, Vivette; Scott, Larkin Ridgway 4 2001 Nonelliptic approximation of a class of partial differential equations with Neumann boundary condition. Zbl 0368.65055Girault, V. 4 1976 A stable enriched Galerkin element for the Stokes problem. Zbl 1395.65072Chaabane, Nabil; Girault, Vivette; Riviere, Beatrice; Thompson, Travis 4 2018 A finite element method for degenerate two-phase flow in porous media. II: Convergence. Zbl 1481.65183Girault, Vivette; Riviere, Beatrice; Cappanera, Loic 4 2021 A posteriori error estimates for Darcy’s problem coupled with the heat equation. Zbl 1434.65226Dib, Séréna; Girault, Vivette; Hecht, Frédéric; Sayah, Toni 4 2019 Finite element approximation of a strain-limiting elastic model. Zbl 1465.74156Bonito, Andrea; Girault, Vivette; Süli, Endre 4 2020 Upwind discretizations of a steady grade-two fluid model in two dimensions. Zbl 1034.35110Girault, V.; Scott, L. R. 3 2002 Variational and classical solutions of a family of fluids of grade two. (Solutions variationnelles et classiques d’une famille de fluides de grade deux.) Zbl 0853.76003Cioranescu, Doina; Girault, Vivette 3 1996 A finite element problem issued from fictious domain techniques. Zbl 1002.65127Bernardi, C.; Girault, V.; Hecht, F.; Kawarada, H.; Pironneau, O. 3 2001 A finite element method for degenerate two-phase flow in porous media. I. Well-posedness. Zbl 1482.65181Girault, Vivette; Riviere, Beatrice; Cappanera, Loic 3 2021 Numerical methods for grade-two fluid models: finite-element discretizations and algorithms. Zbl 1318.76009Girault, Vivette; Hecht, Frédéric 3 2011 Curl-conforming finite element methods for Navier-Stokes equations with nonstandard boundary conditions in \({\mathcal R}^ 3\). Zbl 0702.76037Girault, V. 3 1990 Strong convergence of the discontinuous Galerkin scheme for the low regularity miscible displacement equations. Zbl 1457.76161Girault, Vivette; Li, Jizhou; Rivière, Beatrice M. 3 2017 Analysis of Lavrentiev-finite element methods for data completion problems. Zbl 1444.65035Ben Belgacem, F.; Girault, V.; Jelassi, F. 2 2018 A reduced discrete inf-sup condition in \(L^p\) for incompressible flows and application. Zbl 1321.35154Chacón Rebollo, Tomás; Girault, Vivette; Mármol, Macarena Gómez; Muñoz, Isabel Sánchez 2 2015 The divergence, curl and Stokes operators in exterior domains of \(\mathbb{R}^ 3\). Zbl 0837.35115Girault, Vivette 2 1993 On Friedrichs constant and Horgan-Payne angle for LBB condition. Zbl 1360.35174Dauge, Monique; Bernardi, Christine; Costabel, Martin; Girault, Vivette 2 2014 Spectral methods for the Stokes problem in stream-function formulation. Zbl 0765.76059Bernardi, Christine; Coppoletta, Giuseppe; Girault, Vivette; Maday, Yvon 1 1990 Weighted Sobolev spaces and Laplace’s equation in \({\mathbb{R}{}}^ n\). II. (Espaces de Sobolev avec poids et équation de Laplace dans \({\mathbb{R}{}}^ n\). II.) Zbl 0793.46013Amrouche, Chérif; Girault, Vivette; Giroire, Jean 1 1992 Solutions of a two-dimensional grade-two fluid model with a tangential boundary condition on non-smooth domains. Zbl 1031.76520Girault, Vivette; Scott, Ridgway 1 1998 Regularized finite element discretizations of a grade-two fluid model. Zbl 1072.76036Amara, M.; Bernardi, C.; Girault, V.; Hecht, F. 1 2005 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 On Oldroyd models without explicit dissipation. Zbl 1448.76019Girault, V.; Scott, L. Ridgway 1 2018 A mixed finite element method for the stationary Stokes equations. Zbl 0387.76029Girault, V. 1 1978 Full discretization of Cauchy’s problem by Lavrentiev-finite element method. Zbl 07498293Ben Belgacem, Faker; Girault, Vivette; Jelassi, Faten 1 2022 A finite element method for degenerate two-phase flow in porous media. II: Convergence. Zbl 1481.65183Girault, Vivette; Riviere, Beatrice; Cappanera, Loic 4 2021 A finite element method for degenerate two-phase flow in porous media. I. Well-posedness. Zbl 1482.65181Girault, Vivette; Riviere, Beatrice; Cappanera, Loic 3 2021 A fully coupled scheme using virtual element method and finite volume for poroelasticity. Zbl 1434.86001Coulet, Julien; Faille, Isabelle; Girault, Vivette; Guy, Nicolas; Nataf, Frédéric 9 2020 A posteriori error estimates for Biot system using enriched Galerkin for flow. Zbl 1506.76075Girault, Vivette; Lu, Xueying; Wheeler, Mary F. 7 2020 Finite element approximation of a strain-limiting elastic model. Zbl 1465.74156Bonito, Andrea; Girault, Vivette; Süli, Endre 4 2020 Mixed formulation of a linearized lubrication fracture model in a poro-elastic medium. Zbl 1416.35263Girault, Vivette; Wheeler, Mary F.; Kumar, Kundan; Singh, Gurpreet 4 2019 A posteriori error estimates for Darcy’s problem coupled with the heat equation. Zbl 1434.65226Dib, Séréna; Girault, Vivette; Hecht, Frédéric; Sayah, Toni 4 2019 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 stable enriched Galerkin element for the Stokes problem. Zbl 1395.65072Chaabane, Nabil; Girault, Vivette; Riviere, Beatrice; Thompson, Travis 4 2018 Analysis of Lavrentiev-finite element methods for data completion problems. Zbl 1444.65035Ben Belgacem, F.; Girault, V.; Jelassi, F. 2 2018 On Oldroyd models without explicit dissipation. Zbl 1448.76019Girault, V.; Scott, L. Ridgway 1 2018 Convergence of IPDG for coupled time-dependent Navier-Stokes and Darcy equations. Zbl 1432.65145Chaabane, Nabil; Girault, Vivette; Puelz, Charles; Riviere, Beatrice 7 2017 Strong convergence of the discontinuous Galerkin scheme for the low regularity miscible displacement equations. Zbl 1457.76161Girault, Vivette; Li, Jizhou; Rivière, Beatrice M. 3 2017 Convergence of iterative coupling of geomechanics with flow in a fractured poroelastic medium. Zbl 1391.76650Girault, Vivette; Kumar, Kundan; Wheeler, Mary F. 38 2016 Mechanics and mathematics of fluids of the differential type. Zbl 1365.76001Cioranescu, D.; Girault, V.; Rajagopal, K. R. 20 2016 Continuity properties of the inf-sup constant for the divergence. Zbl 1339.35230Bernardi, Christine; Costabel, Martin; Dauge, Monique; Girault, Vivette 9 2016 Analysis of a coupled fluid-structure model with applications to hemodynamics. Zbl 1343.35184Chacón Rebollo, T.; Girault, V.; Murat, F.; Pironneau, O. 9 2016 Strong convergence of discrete DG solutions of the heat equation. Zbl 1352.65290Girault, Vivette; Li, Jizhou; Rivière, Beatrice 6 2016 A lubrication fracture model in a poro-elastic medium. Zbl 1309.76194Girault, V.; Wheeler, M. F.; Ganis, B.; Mear, M. E. 35 2015 Max-norm estimates for Stokes and Navier-Stokes approximations in convex polyhedra. Zbl 1401.76087Girault, V.; Nochetto, R. H.; Scott, L. R. 18 2015 A reduced discrete inf-sup condition in \(L^p\) for incompressible flows and application. Zbl 1321.35154Chacón Rebollo, Tomás; Girault, Vivette; Mármol, Macarena Gómez; Muñoz, Isabel Sánchez 2 2015 Mortar multiscale finite element methods for Stokes-Darcy flows. Zbl 1396.76051Girault, Vivette; Vassilev, Danail; Yotov, Ivan 43 2014 Error analysis for a monolithic discretization of coupled Darcy and Stokes problems. Zbl 1302.76101Girault, V.; Kanschat, G.; Rivière, B. 14 2014 On Friedrichs constant and Horgan-Payne angle for LBB condition. Zbl 1360.35174Dauge, Monique; Bernardi, Christine; Costabel, Martin; Girault, Vivette 2 2014 Time-dependent coupling of Navier–Stokes and Darcy flows. Zbl 1267.76096Cesmelioglu, Aycil; Girault, Vivette; Rivière, Béatrice 29 2013 A high order term-by-term stabilization solver for incompressible flow problems. Zbl 1426.76234Chacón Rebollo, T.; Gómez Mármol, M.; Girault, V.; Sánchez Muñoz, I. 17 2013 Domain decomposition for poroelasticity and elasticity with DG jumps and mortars. Zbl 1216.35153Girault, V.; Pencheva, G.; Wheeler, M. F.; Wildey, T. 16 2011 Mixed formulation, approximation and decoupling algorithm for a penalized nematic liquid crystals model. Zbl 1228.35176Girault, V.; Guillén-González, F. 13 2011 Numerical methods for grade-two fluid models: finite-element discretizations and algorithms. Zbl 1318.76009Girault, Vivette; Hecht, Frédéric 3 2011 \(L^p\) and \(W^{1,p}\) regularity of the solution of a steady transport equation. (Régularité dans \(L^p\) et \(W^{1,p}\) de la solution d’une équation de transport stationnaire.) Zbl 1200.35207Girault, Vivette; Tartar, Luc 7 2010 Finite element discretization of Darcy’s equations with pressure-dependent porosity. Zbl 1271.76166Girault, Vivette; Murat, François; Salgado, Abner 7 2010 On a time-dependent transport equation in a Lipschitz domain. Zbl 1217.35048Girault, V.; Scott, L. Ridgway 5 2010 DG approximation of coupled Navier-Stokes and Darcy equations by Beaver-Joseph-Saffman interface condition. Zbl 1406.76082Girault, Vivette; Rivière, Béatrice 116 2009 A second order accuracy for a full discretized time-dependent Navier-Stokes equations by a two-grid scheme. Zbl 1407.76111Abboud, Hyam; Girault, Vivette; Sayah, Toni 28 2009 Domain decomposition for linear elasticity with DG jumps and mortars. Zbl 1227.74069Girault, Vivette; Pencheva, Gergina V.; Wheeler, Mary F.; Wildey, Tim M. 7 2009 Numerical discretization of a Darcy-Forchheimer model. Zbl 1143.76035Girault, V.; Wheeler, M. F. 50 2008 Coupling discontinuous Galerkin and mixed finite element discretizations using mortar finite elements. Zbl 1165.65075Girault, Vivette; Sun, Shuyu; Wheeler, Mary F.; Yotov, Ivan 28 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 Discontinuous Galerkin methods. Zbl 1149.65323Girault, Vivette; Wheeler, Mary F. 6 2008 Finite elements approximation of second order linear elliptic equations in divergence form with right-hand side in \(L^1\). Zbl 1144.65072Casado-Díaz, J.; Chacón Rebollo, T.; Girault, V.; Gómez Mármol, M.; Murat, F. 18 2007 On a time-dependent grade-two fluid model in two dimensions. Zbl 1122.76009Girault, V.; Saadouni, M. 7 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 Discontinuous finite element methods for incompressible flows on subdomains with non-matching interfaces. Zbl 1121.76038Rivière, Béatrice; Girault, Vivette 14 2006 One time-step finite element discretization of the equation of motion of two-fluid flows. Zbl 1089.76032Girault, V.; López, H.; Maury, B. 7 2006 A discontinuous Galerkin method with nonoverlapping domain decomposition for the Stokes and Navier-Stokes problems. Zbl 1057.35029Girault, Vivette; Rivière, Béatrice; Wheeler, Mary F. 94 2005 Maximum-norm stability of the finite element Stokes projection. Zbl 1210.76051Girault, V.; Nochetto, R. H.; Scott, R. 31 2005 A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations. Zbl 1085.76037Girault, Vivette; Rivière, Béatrice; Wheeler, Mary F. 19 2005 Two-grid finite element scheme for the fully discrete time-dependent Navier-Stokes problem. Zbl 1078.65083Abboud, Hyam; Girault, Vivette; Sayah, Toni 5 2005 Regularized finite element discretizations of a grade-two fluid model. Zbl 1072.76036Amara, M.; Bernardi, C.; Girault, V.; Hecht, F. 1 2005 Stability of the finite element Stokes projection in \(W^{1,\infty}\). Zbl 1049.65118Girault, Vivette; Nochetto, Ricardo H.; Scott, Ridgway 6 2004 A domain decomposition and mixed method for a linear parabolic boundary value problem. Zbl 1062.65101Girault, V.; Glowinski, R.; López, H. 6 2004 A quasi-local interpolation operator preserving the discrete divergence. Zbl 1072.65014Girault, V.; Scott, L. R. 41 2003 A posteriori analysis of a penalty method and application to the Stokes problem. Zbl 1050.65099Bernardi, C.; Girault, V.; Hecht, F. 12 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 Hermite interpolation of nonsmooth functions preserving boundary conditions. Zbl 1002.65129Girault, V.; Scott, L. R. 25 2002 Inf-sup condition for the 3-D \(P_2\)-iso-\(P_1\) Taylor-Hood finite element; application to Maxwell equations. (Condition inf-sup pour l’élément fini de Taylor-Hood \(P_2\)-iso-\(P_1\), 3-D; application aux équations de Maxwell.) Zbl 1021.78009Ciarlet, Patrick jun.; Girault, Vivette 14 2002 Upwind discretizations of a steady grade-two fluid model in two dimensions. Zbl 1034.35110Girault, V.; Scott, L. R. 3 2002 A priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems. Zbl 1010.65045Rivière, Béatrice; Wheeler, Mary F.; Girault, Vivette 188 2001 Two-grid finite element schemes for the transient Navier-Stokes problem. Zbl 1032.76032Girault, Vivette; Lions, Jacques-Louis 73 2001 Two-grid finite-element schemes for the steady Navier-Stokes problem in polyhedra. Zbl 0997.76043Girault, V.; Lions, J.-L. 64 2001 A boundary multiplier/fictitious domain method for the steady incompressible Navier-Stokes equations. Zbl 1002.76067Girault, V.; Glowinski, R.; López, H.; Vila, J.-P. 10 2001 Finite element discretizations of a two-dimensional grade-two fluid model. Zbl 1032.76033Girault, Vivette; Scott, Larkin Ridgway 4 2001 A finite element problem issued from fictious domain techniques. Zbl 1002.65127Bernardi, C.; Girault, V.; Hecht, F.; Kawarada, H.; Pironneau, O. 3 2001 Pointwise decay of solutions and of higher derivatives to Navier-Stokes equations. Zbl 0986.35085Amrouche, Cherif; Girault, Vivette; Schonbek, Maria Elena; Schonbek, Tomas P. 20 2000 Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I. Zbl 0951.65108Rivière, Béatrice; Wheeler, Mary F.; Girault, Vivette 181 1999 Analysis of a two-dimensional grade-two fluid model with a tangential boundary condition. Zbl 0961.35116Girault, V.; Scott, L. R. 25 1999 A fictitious-domain method with distributed multiplier for the Stokes problem. Zbl 0954.35127Girault, Vivette; Glowinski, Roland; Pan, T. W. 13 1999 Vector potentials in three-dimensional non-smooth domains. Zbl 0914.35094Amrouche, C.; Bernardi, C.; Dauge, M.; Girault, V. 388 1998 A local regularization operator for triangular and quadrilateral finite elements. Zbl 0913.65007Bernardi, C.; Girault, V. 85 1998 Solutions of a two-dimensional grade-two fluid model with a tangential boundary condition on non-smooth domains. Zbl 1031.76520Girault, Vivette; Scott, Ridgway 1 1998 Dirichlet and Neumann exterior problems for the \(n\)-dimensional Laplace operator. An approach in weighted Sobolev spaces. Zbl 0878.35029Amrouche, C.; Girault, V.; Giroire, J. 74 1997 Weak and classical solutions of a family of second grade fluids. Zbl 0891.76005Cioranescu, D.; Girault, V. 51 1997 Error analysis of a finite element realization of a fictitious domain/domain decomposition method for elliptic problems. Zbl 0878.65087Girault, V.; Glowinski, R.; Lopez, H. 1 1997 Finite-element error estimates for the MAC scheme. Zbl 0853.76037Girault, V.; Lopez, H. 35 1996 Variational and classical solutions of a family of fluids of grade two. (Solutions variationnelles et classiques d’une famille de fluides de grade deux.) Zbl 0853.76003Cioranescu, Doina; Girault, Vivette 3 1996 Error analysis of a fictitious domain method applied to a Dirichlet problem. Zbl 0843.65076Girault, V.; Glowinski, R. 67 1995 A local projection operator for quadrilateral finite elements. Zbl 0856.65128Girault, V. 5 1995 Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension. Zbl 0823.35140Amrouche, Chérif; Girault, Vivette 137 1994 Weighted Sobolev spaces for Laplace’s equation in \(\mathbb{R}^ n\). Zbl 0836.35038Amrouche, C.; Girault, V.; Giroire, J. 57 1994 The Stokes problem and vector potential operator in three-dimensional exterior domains: An approach in weighted Sobolev spaces. Zbl 0831.35125Girault, V. 15 1994 The divergence, curl and Stokes operators in exterior domains of \(\mathbb{R}^ 3\). Zbl 0837.35115Girault, Vivette 2 1993 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 A stream-function–vorticity variational formulation for the exterior Stokes problem in weighted Sobolev spaces. Zbl 0761.35083Girault, V.; Giroire, J.; Sequeira, A. 13 1992 The gradient, divergence, curl and Stokes operators in weighted Sobolev spaces of \(\mathbb{R}^ 3\). Zbl 0779.35088Girault, V. 12 1992 Generalized Stokes problems. (Problèmes généralisés de Stokes.) Zbl 0790.35084Amrouche, Chérif; Girault, Vivette 10 1992 Weighted Sobolev spaces and Laplace’s equation in \(\mathbb{R}^ n\). I. (Espaces de Sobolev avec poids et équation de Laplace dans \(\mathbb{R}^ n\). I.) Zbl 0801.46035Amrouche, Chérif; Girault, Vivette; Giroire, Jean 4 1992 Weighted Sobolev spaces and Laplace’s equation in \({\mathbb{R}{}}^ n\). II. (Espaces de Sobolev avec poids et équation de Laplace dans \({\mathbb{R}{}}^ n\). II.) Zbl 0793.46013Amrouche, Chérif; Girault, Vivette; Giroire, Jean 1 1992 On the existence and regularity of the solution of Stokes problem in arbitrary dimension. Zbl 0752.35047Amrouche, Chérif; Girault, Vivette 40 1991 A well-posed problem for the exterior Stokes equations in two and three dimensions. Zbl 0731.35078Girault, Vivette; Sequeira, Adelia 30 1991 A stream function-vorticity variational formulation for the exterior Stokes problem in weighted Sobolev spaces. (Formulation variationnelle en fonction courant-tourbillon du problème de Stokes extérieur dans des espaces de Sobolev à poids.) Zbl 0737.35064Girault, Vivette; Giroire, Jean; Sequeira, Adelia 4 1991 Curl-conforming finite element methods for Navier-Stokes equations with nonstandard boundary conditions in \({\mathcal R}^ 3\). Zbl 0702.76037Girault, V. 3 1990 Spectral methods for the Stokes problem in stream-function formulation. Zbl 0765.76059Bernardi, Christine; Coppoletta, Giuseppe; Girault, Vivette; Maday, Yvon 1 1990 Incompressible finite element methods for Navier-Stokes equations with nonstandard boundary conditions in \(R^ 3\). Zbl 0666.76053Girault, V. 32 1988 Finite element methods for Navier-Stokes equations. Theory and algorithms. (Extended version of the 1979 publ.). Zbl 0585.65077Girault, Vivette; Raviart, Pierre-Arnaud 2,026 1986 An analysis of upwind schemes for the Navier-Stokes equations. Zbl 0487.76036Girault, V.; Raviart, P.-A. 12 1982 Finite element approximation of the Navier-Stokes equations. Rev. repr. of the 1st ed. Zbl 0441.65081Girault, V.; Raviart, P.-A. 65 1981 Finite element approximation of the Navier-Stokes equations. Zbl 0413.65081Girault, V.; Raviart, P.-A. 664 1979 An analysis of a mixed finite element method for the Navier-Stokes equations. Zbl 0396.65070Girault, V.; Raviart, P. A. 410 1979 A mixed finite element method for the stationary Stokes equations. Zbl 0387.76029Girault, V. 1 1978 ...and 4 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 4,300 Authors 105 He, Yinnian 63 Girault, Vivette 60 Amrouche, Chérif 59 Bernardi, Christine 51 Gatica, Gabriel N. 48 Li, Jian 41 Wheeler, Mary Fanett 40 Rivière, Beatrice M. 39 Nicaise, Serge 38 Gunzburger, Max D. 36 Ciarlet, Patrick jun. 36 Shang, Yueqiang 35 Ruiz-Baier, Ricardo 33 Ye, Xiu 32 Oyarzúa, Ricardo 29 Ciarlet, Philippe Gaston 29 Rodríguez, Rodolfo 29 Rui, Hongxing 28 Sun, Shuyu 27 Chen, Zhangxin 27 Duan, Huoyuan 26 He, Xiaoming 25 Hecht, Frédéric 25 Hiptmair, Ralf 24 Burman, Erik 24 Chacón Rebollo, Tomás 24 Hou, Yanren 24 Zhang, Shangyou 23 Barrenechea, Gabriel R. 23 Carstensen, Carsten 23 Huang, Pengzhan 23 Layton, William J. 23 Luo, Zhendong 22 Rebholz, Leo G. 21 Mora, David 21 Schötzau, Dominik 20 Brenner, Susanne Cecelia 20 Sayas, Francisco-Javier 20 Yotov, Ivan 20 Zou, Jun 19 Boffi, Daniele 19 Guillén González, Francisco M. 19 Kumar, Kundan 19 Süli, Endre E. 18 Ben Belgacem, Faker 18 Feng, Xinlong 18 Guermond, Jean-Luc 18 Li, Kaitai 18 Quarteroni, Alfio M. 18 Ruas, Vitoriano 18 Shi, Dongyang 17 Kaya, Songul 17 Linke, Alexander 17 Lube, Gert 17 Olshanskii, Maxim A. 17 Pasciak, Joseph E. 17 Salgado, Abner J. 17 Sayah, Toni 17 Wang, Junping 17 Xu, Jinchao 16 Feng, Minfu 16 Gastaldi, Lucia 16 Ma, Yichen 16 Meddahi, Salim 16 Park, Eun-Jae 16 Rojas-Medar, Marko Antonio 16 Tobiska, Lutz 16 Zheng, Haibiao 15 Beirão da Veiga, Lourenço 15 Boulmezaoud, Tahar Zamène 15 Chorfi, Nejmeddine 15 Cockburn, Bernardo 15 Glowinski, Roland 15 Guzmán, Johnny 15 John, Volker 15 Li, Jichun 15 Neff, Patrizio 15 Pani, Amiya Kumar 15 Zhang, Tong 14 An, Rong 14 Bramble, James H. 14 Buffa, Annalisa 14 Ern, Alexandre 14 Han, Weimin 14 Huang, Yunqing 14 Maday, Yvon 14 Mao, Shipeng 14 Mei, Liquan 14 Stenberg, Rolf 14 Vougalter, Vitali 14 Yang, Suh-Yuh 13 Bermúdez, Alfredo 13 Chung, Tsz Shun Eric 13 Hu, Jun 13 Larson, Mats G. 13 Lin, Tao 13 Merdon, Christian 13 Nochetto, Ricardo Horacio 13 Perugia, Ilaria 13 Reddy, B. 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