Computational Methods for Option Pricing, SIAM, 2005. ,
DOI : 10.1137/1.9780898717495
URL : https://hal.archives-ouvertes.fr/hal-00111740
Commande optimale, 1982. ,
Concepion optimale de structures, 2007. ,
Boundary Value Problems in Mechanics of Nonhomogeneous Fluids, 1993. ,
A stable finite element for the stokes equations, Calcolo, vol.21, issue.4, pp.337-344, 1984. ,
DOI : 10.1007/BF02576171
The finite element method with Lagrangian multipliers, Numerische Mathematik, vol.12, issue.3, pp.179-192, 1973. ,
DOI : 10.1007/BF01436561
Dynamic Programming, 1957. ,
Error estimates for finite element method solution of the Stokes problem in the primitive variables, Numerische Mathematik, vol.65, issue.2, pp.211-224, 1979. ,
DOI : 10.1007/BF01399555
Approximations spectrales deprobì emes aux limites elliptiques, 1992. ,
IntroductionàIntroduction`Introductionà la Dynamique des Milieux Continus. ´ Ecole de Printemps, GDR Matériaux Vitreux, 2003. ,
Application des capteurs thermiques implantés pour la détection du profil de gelée dans la cuve d'´ electrolyse. Master's thesis, 2001. ,
Nonlinear Waves with Electromagnetic Interactions in Aluminium Electrolysis Cells, Progress in Fluid Flow Research : Turbulence and Applied MHD Progress in Astronautics and Aeronautics, pp.833-848, 1998. ,
Long Waves Instability of Liquid Metal-Electrolyte Interface in Aluminium Electrolysis Cells : a Generalization of Sele's criterion, Eur. J. Mech. B, vol.13, pp.33-56, 1994. ,
Optimisation numérique, 1997. ,
Analyse fonctionnelle. Théorie et applications, 2000. ,
On the Existence, Uniqueness and Approximation of Saddle-Point Problems Arising from Lagrange Multipliers, pp.129-151, 1974. ,
Infinite-Dimensional Optimization and Optimal Design. Lectures Notes 285J, Departement of Mathematics, 2003. ,
Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations, ESAIM: Control, Optimisation and Calculus of Variations, vol.8, pp.513-554, 2002. ,
DOI : 10.1051/cocv:2002050
???ber die partiellen Differenzengleichungen der mathematischen Physik, Uber die partiellen Differenzengleichungen der Matematischen Physik, pp.32-74, 1928. ,
DOI : 10.1007/BF01448839
Viscosity solutions of Hamilton-Jacobi equations, Transactions of the American Mathematical Society, vol.277, issue.1, pp.1-42, 1983. ,
DOI : 10.1090/S0002-9947-1983-0690039-8
Simulation numérique en C++, 2003. ,
Analyse mathématique et calcul numérique pour les sciences et les techniques, 1984. ,
Stability of interfacial waves in aluminium reduction cells, Journal of Fluid Mechanics, vol.362, pp.273-295, 1998. ,
DOI : 10.1017/S0022112098001025
Shapes and Geometries, Differential Calculus, and Optimization. SIAM Advances in Design and Control, 2001. ,
DOI : 10.1137/1.9780898719826
Modelling for Instabilities in Hall-Héroult Cells : Mathematical and Numerical Aspects, Magnetohydrodynamics in Process Metallurgy, pp.107-110, 1991. ,
Ordinary differential equations, transport theory and Sobolev spaces, Inventiones Mathematicae, vol.307, issue.3, pp.511-547, 1989. ,
DOI : 10.1007/BF01393835
Inéquations en Thermoélasticité et Magnétohydrodynamique, Arch. of Rat. Mech. Anal, vol.46, pp.241-279, 1972. ,
Theory and Practice of Finite Elements, 2004. ,
DOI : 10.1007/978-1-4757-4355-5
Couplage fluide-structure : un modèle simplifié en dimension 1, C. R. Acad. Sci. Paris, Série I, vol.318, pp.275-281, 1994. ,
Analyse numérique. Notes d'optimisation. ´ Ecole Polytechnique, Ellipses, 1988. ,
Existence and Smoothness of the Navier-Stokes Equation, Clay Mathematics Institute, 2000. ,
Very high-speed computing systems, Proceedings of the IEEE, pp.1901-1909, 1966. ,
DOI : 10.1109/PROC.1966.5273
Numerical Treatment of Defective Boundary Conditions for the Navier--Stokes Equations, SIAM Journal on Numerical Analysis, vol.40, issue.1, pp.376-401, 2002. ,
DOI : 10.1137/S003614290038296X
URL : https://hal.archives-ouvertes.fr/inria-00072539
Stabilized finite element methods: II. The incompressible Navier-Stokes equations, 36] A.V. Fursikov. Optimal Control of Distributed Systems. Theory and Applications, pp.209-233, 1992. ,
DOI : 10.1016/0045-7825(92)90041-H
Probì emes mathématiques et numériques posés par la modélisation de l'´ electrolyse de l'aluminium, 1998. ,
Existence of Solution for a Density-Dependent Magnetohydrodynamic Equation, Advances in Differential Equations, pp.427-452, 1997. ,
URL : https://hal.archives-ouvertes.fr/hal-00690237
Mathematical methods for the Magnetohydrodynamics of liquid metals, 2006. ,
DOI : 10.1093/acprof:oso/9780198566656.001.0001
Linear Versus Nonlinear Approaches for the Stability Analysis of Aluminium Production Cells, Proceedings of the European Conference on Computational Fluid Dynamics (ECCOMAS), 2006. ,
Finite Element Methods for the Incompressible Navier-Stokes Equations, 1986. ,
Computer Calculation of Magnetic Effects in the Bath of Aluminium Cells. Transactions of the Metallurgical Society of Aime, pp.1161-1166, 1967. ,
Exact and Approximate Controllability for Distributed Parameter Systems (part I) Acta Numerica, pp.269-378, 1994. ,
Exact and Approximate Controllability for Distributed Parameter Systems (part II) Acta Numerica, pp.159-333, 1996. ,
On the existence, uniqueness, and finite element approximation of solutions of the equations of stationary, incompressible magnetohydrodynamics, EDP Sciences / CNRSÉditions CNRS´CNRSÉditions, pp.523-563, 1991. ,
DOI : 10.1090/S0025-5718-1991-1066834-0
A non-conforming P 1 basis with free divergence in R 3, 1983. ,
Functional Analysis and Semi-Groups, 1957. ,
DOI : 10.1090/coll/031
An arbitrary Lagrangian-Eulerian computing method for all flow speeds, Journal of Computational Physics, vol.14, issue.3, pp.227-253, 1974. ,
DOI : 10.1016/0021-9991(74)90051-5
Navier-Stokes Equations Using Mixed Interpolation, 1974. ,
Boundary optimal control of MHD flows, Applied Mathematics & Optimization, vol.25, issue.2, pp.143-162, 1995. ,
DOI : 10.1007/BF01185228
A new finite element formulation for computational fluid dynamics: V. Circumventing the babu??ka-brezzi condition: a stable Petrov-Galerkin formulation of the stokes problem accommodating equal-order interpolations, Computer Methods in Applied Mechanics and Engineering, vol.59, issue.1, pp.85-99, 1986. ,
DOI : 10.1016/0045-7825(86)90025-3
On the general theory of control systems, Proc. 1st IFAC Congress, pp.481-492, 1960. ,
DOI : 10.1109/TAC.1959.1104873
METIS : A Software Package for Partitioning Unstructured Graphs, Partitioning Meshes, and Computing Fill-Reducing Orderings of Sparse Matrices, 1998. ,
Nonlinear Programming, Proceedings of Second Berkeley Symposium on Mathematical Statistics and Probability, pp.481-492, 1961. ,
The Variational Principles of Dynamics Advanced Series in Mathematical Physics, World Scientific, 1992. ,
´ Electrodynamique des milieux continus, 1990. ,
Mathematical Models of Turbulence, 1972. ,
Parabolic equations. Contributions to the Theory of Partial Differential Equations, 1954. ,
´ Etude de diverseséquationsdiverseséquations intégrales non linéaires et de quelquesprobì emes que pose l'hydrodynamique, J. Math. Pures Appl, vol.12, pp.1-82, 1933. ,
DOI : 10.1007/bf01350150
Optimal Control Theory for Infinite Dimensional Systems, 1995. ,
DOI : 10.1007/978-1-4612-4260-4
Quelques méthodes de résolution desprobì emes aux limites non linéaires, Dunod et Gauthier-Villars, 1969. ,
Optimal Control of Systems Governed by Partial Differential Equations, 1971. ,
DOI : 10.1007/978-3-642-65024-6
Exact Controllability, Stabilization and Perturbations for Distributed Systems, SIAM Review, vol.30, issue.1, 1994. ,
DOI : 10.1137/1030001
Non-Homogeneous Boundary Value Problems and Applications, 1971. ,
DOI : 10.1007/978-3-642-65161-8
Mathematical Topics in Fluid Mechanics, 1996. ,
Linear and Nonlinear Programming, 2003. ,
DOI : 10.1007/978-3-319-18842-3
SparseLib++ Reference Guide, 1996. ,
Guidelines for the usage of incomplete decompositions in solving sets of linear equations as they occur in practical problems, Journal of Computational Physics, vol.44, issue.1, pp.44-134, 1981. ,
DOI : 10.1016/0021-9991(81)90041-3
Applied Shape Optimization for Fluids, 2001. ,
DOI : 10.1093/acprof:oso/9780199546909.001.0001
URL : https://hal.archives-ouvertes.fr/hal-00385714
An Analysis of the Hydrodynamics of Aluminum Reduction Cells, Journal of The Electrochemical Society, vol.131, issue.10, pp.2251-2259, 1984. ,
DOI : 10.1149/1.2115235
Stability of Aluminium Cells : a New Approach, Light Metals, pp.359-364, 1986. ,
Simulation numérique des instabilités magnétohydrodynamiques dans les cuves de production d'aluminium. Master's thesis http ://mhd.selfip.info/com/memoire-rectoverso.pdf. [77] J.-C. Nédélec. A New Family of Mixed Finite Elements in R 3, Numer. Math, vol.50, pp.57-81, 1986. ,
A Method of Computation for Structural Dynamics, Proceedings of ASME Conference. ASME, 1959. ,
Algorithmes de contrôle d'interface libre. Implémentation sur un modèle MHD linéaire, Congrès National d'Analyse Numérique (CANUM), 2006. ,
Simulations numériques sous Mistral &Probì emes de contrôle d'interface libre, 2005. ,
Finite Element Methods for Fluids, 1989. ,
Numerical Approximation of Partial Differential Equations, 1997. ,
IntroductionàIntroduction`Introductionà l'analyse numérique deséquationsdeséquations aux dérivées partielles, 1998. ,
Iterative Methods for Sparse Linear Systems, 1996. ,
DOI : 10.1137/1.9780898718003
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems, SIAM Journal on Scientific and Statistical Computing, vol.7, issue.3, pp.856-869, 1986. ,
DOI : 10.1137/0907058
Simulation numérique des phénomènes thermiques et magnétohydrodynaiques dans une cellule de Hall-Héroult, 2005. ,
Handbook of Continuum Mechanics, 2001. ,
DOI : 10.1007/978-3-642-56542-7
Analysis of Magnetohydrodynamic Instabilities in Aluminium Reduction Cells. Light Metals, pp.313-322, 1994. ,
Instabilities of the Metal Surface in Electrolytic Cells, Light Metals, pp.7-24, 1977. ,
Some Mathematical Questions Related to the MHD Equations, Communications in Pure and Applied Mathematics, vol.XXXVI, pp.635-664, 1983. ,
URL : https://hal.archives-ouvertes.fr/inria-00076373
Stability of fluid layers carrying a normal electric current, Journal of Fluid Mechanics, vol.156, issue.-1, pp.223-236, 1985. ,
DOI : 10.1017/S0022112085002063
Interfacial instability due to MHD mode coupling in aluminium reduction cells, Journal of Fluid Mechanics, vol.none, issue.-1, pp.343-359, 1994. ,
DOI : 10.1017/S0022112085002063
Infinite-Dimensional Dynamical Systems in Mechanics and Physics, 1988. ,
Contrôle optimal. Théorie et applications, 2005. ,
Official Aztec User's Guide, 1999. ,
Magnetics and Metal Pad Instabilities, Light Metals, pp.581-591, 1985. ,
DOI : 10.1007/978-3-319-48156-2_47
Functional Analysis, 1965. ,
Shallow Water Model of flows in Hall-Héroult Cells, Light Metals, pp.335-340, 2004. ,