He headed the mathematics department of the Laboratoire central des Ponts et Chaussées (1966-1973) and was a lecturer at the École polytechnique (1967-1985), professor at the École nationale des Ponts et Chaussées (1978-1987), consultant at INRIA (1974-1994). From 1974 to 2002, he was a professor at the University of Pierre et Marie Curie where he directed the laboratory of Numerical Analysis from 1981 to 1992.
Numerical analysis of finite difference methods and general variational approximation methods: In his doctoral theses and early publications, Philippe Ciarlet made innovative contributions to the numerical approximation by variational methods of problems with non-linear monotonous boundaries,[6] and introduced the concepts of discrete Green functions and the discrete maximum principle,[7][8] which have since proved to be fundamental in numerical analysis.
Interpolation theory: Philippe Ciarlet has made innovative contributions, now "classical" to Lagrange and Hermite interpolation theory in R^n, notably through the introduction of the notion of multipoint Taylor formulas.[9] This theory plays a fundamental role in establishing the convergence of finite element methods.
Numerical analysis of the finite element method: Philippe Ciarlet is well known for having made fundamental contributions in this field, including convergence analysis, the discrete maximum principle, uniform convergence, analysis of curved finite elements, numerical integration, non-conforming macroelements for plate problems, a mixed method for the biharmonic equation in fluid mechanics, and finite element methods for shell problems. His contributions and those of his collaborators can be found in his well-known book.[10]
Plate modeling by asymptotic analysis and singular disturbance techniques: Philippe Ciarlet is also well known for his leading role in justifying two-dimensional models of linear and non-linear elastic plates from three-dimensional elasticity; in particular, he established convergence in the linear case,[11][12] and justified two-dimensional non-linear models, including the von Kármán and Marguerre-von Karman equations, by the asymptotic development method.[13]
Modeling, mathematical analysis and numerical simulation of "elastic multi-structures" including junctions: This is another entirely new field that Philippe Ciarlet has created and developed, by establishing the convergence of the three-dimensional solution towards that of a "multidimensional" model in the linear case, by justifying the limit conditions for embedding a plate.[14][15]
Modeling and mathematical analysis of "general" shells: Philippe Ciarlet established the first existence theorems for two-dimensional linear shell models, such as those of W.T. Koiter and P.M. Naghdi,[16] and justified the equations of the "bending" and "membrane" shell;[17][18][19] he also established the first rigorous justification of the "shallow" two-dimensional linear shell equations and of Koiter equations, using asymptotic analysis techniques; he also obtained a new theory of existence for non-linear shell equations.
Non-linear elasticity: Philippe Ciarlet proposed a new energy function that is polyconvex (as defined by John Ball), and has proven to be very effective because it is "adjustable" to any given isotropic elastic material;[20] he has also made important and innovative contributions to the modelling of contact and non-interpenetration in three-dimensional non-linear elasticity.[21] He also proposed and justified a new non-linear Koiter-type model for non-linearly elastic hulls.
Non-linear inequalities of Korn on a surface: Philippe Ciarlet gave several new proofs of the fundamental theorem of surface theory, concerning the reconstruction of a surface according to its first and second fundamental forms. He was the first to show that a surface continuously varies according to its two fundamental forms, for different topologies,[22] notably by introducing a new idea, that of non-linear Korn inequalities on a surface, another notion that he essentially created and developed with his collaborators.[23]
Functional analysis: Philippe Ciarlet established weak forms of Poincaré's lemma and conditions of compatibility of Saint Venant, in Sobolev's spaces with negative exponents; he established that there are deep relationships between Jacques-Louis Lions' lemma, Nečas's inequality, Rham's theorem, and Bogovskii's theorem, which provide new methods to establish these results.[24]
Intrinsic methods in linearized elasticity: Philippe Ciarlet has developed a new field, that of the mathematical justification of "intrinsic" methods in linearized elasticity, where the linearized metric tensor and the linearized tensor of curvature change are the new, and only, unknowns:[25] This approach, whether for three-dimensional elasticity or for plate and shell theories, requires an entirely new approach, based mainly on the compatibility conditions of Saint-Venant and Donati in Sobolev spaces.
Intrinsic methods in non-linear elasticity: Philippe Ciarlet has developed a new field, that of the mathematical justification of "intrinsic" methods in non-linear elasticity. This approach makes it possible to obtain new existence theorems in three-dimensional non-linear elasticity.[26]
Teaching and research books: Philippe Ciarlet has written several textbooks that are now "classics ",[10][27][28][29] as well as several "reference" research books.[30][31][32][33]
^Ciarlet, P.G.; Schultz, M.H.; Varga, R.S., « Numerical methods of high-order accuracy for nonlinear boundary value problems. I. One dimensional problem », Numer. Math., 9 (1967), p. 394–430
^Ciarlet, P.G., « Discrete variational Green’s function. I », Aequationes Math., 4 (1970), p. 74–82
^Ciarlet, P.G., « Discrete maximum principe for finite-difference operators », Aequationes Math., 4 (1970), p. 338–352
^Ciarlet, P.G.; Raviart, P.A., « General Lagrange and Hermite interpolation in Rn with applications to finite elements methods », Arch. Rational Mech. Anal., 46 (1972), p. 177–199
^ aba et b Ciarlet, P.G., The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, Mathematics and its Applications, 1978
^Ciarlet, P.G.; Destuynder P., « A justification of the two-dimensional linear plate model », J. Mécanique, 18 (1979), p. 315–344
^Ciarlet, P.G.; Kesavan S., « Two-dimensional approximations of three-dimensional eigenvalue problems in plate theory », Comp. Methods in Appl. Mech. and Engineering, 26 (1981), p. 145–172
^Ciarlet, P.G., « A justification of the von Kármán equations », Arch. RationalMech. Anal., 73 (1980), p. 349–389
^Ciarlet, P.G.; Le Dret, H.; Nzengwa, R. J., « Functions between three-dimensional and two- dimensional linearly elastic structures », J. Math. Pures Appl., 68 (1989), p. 261–295
^Ciarlet, P.G., Plates and Junctions in Elastic Multi-Structures : An Asymptotic Analysis, Paris et Heidelberg, Masson & Springer-Verlag, 1990
^Bernadou, M.; Ciarlet, P.G.; Miara, B., « Existence theorems for two-dimensional linear shell theories », J. Elasticity, 34 (1994), p. 111–138
^Ciarlet, P.G.; Lods, V., « Asymptotic analysis of linearly elastic shells. I. Justification of membrane shells equations », Arch. Rational Mech. Anal., 136 (1996), p. 119-161
^Ciarlet, P.G.; Lods, V.; Miara, B., « Asymptotic analysis of linearly elastic shells. II. Justification of flexural shells », Arch. Rational Mech. Anal., 136 (1996), p. 163-190
^Ciarlet P.G.; Lods, V., « Asymptotic analysis of linearly elastic shells : "Generalized membrane shells" », J. Elasticity, 43 (1996), p. 147–188
^Ciarlet, P.G.; Geymonat, G., « Sur les lois de comportement en élasticité non linéaire compressible », C. R. Acad. Sc. Paris Sér. II, 295 (1982), p. 423-426
^Ciarlet, P.G.; Neˇ Cas, J., « Injectivity and self-contact in nonlinear elasticity », Arch. Rational Mech. Anal., 97 (1987), p. 171–188
^Ciarlet, P.G., « The continuity of a surface as a function of its two fundamental forms », J. Math. Pures Appl., 82 (2003), p. 253-274
^Ciarlet, P.G.; Gratie, L.; Mardare C., « A nonlinear Korn inequality on a surface », J. Math. Pures Appl., 85 (2006), p. 2-16
^Amrouche, C.; Ciarlet, P.G.; Mardare, C., « On a lemma of Jacques-Louis Lions and its relation to other fundamental results », J. Math. Pures Appl., 104 (2015), p. 207-226
^Ciarlet, P.G.; Ciarlet, JR., P., « Direct computation of stresses in planar linearized elasticity », Math. Models Methods Appl. Sci., 19 (2009), p. 1043-1064
^Ciarlet, P.G.; Mardare, C., « Existence theorems in intrinsic nonlinear elasticity », J. Math. Pures Appl., 94 (2010), p. 229-243
^Ciarlet, P.G., Introduction à l’Analyse Numérique Matricielle et à l’Optimisation, Paris, Masson, 1982
^Ciarlet, P.G., An Introduction to Differential Geometry, with Applications to Elasticity, Dordrecht, Springer, 2005
^Ciarlet, P.G., Linear and Nonlinear Functional Analysis with Applications, Philadelphia, SIAM, 2013
^Ciarlet, P.G.; Rabier, P., Les équations de von Kármán, Lectures Notes in Mathematics, Vol.826, Berlin, Springer-Verlag, 1980
^Ciarlet, P.G., Mathematical Elasticity, Vol. I : Three-Dimensional Elasticity, North-Holland, Amsterdam, Series "Studies in Mathematics and its Applications, 1988
^Ciarlet, P.G., Mathematical Elasticity, Vol. II: Theory of Plates, North-Holland, Amsterdam, Series "Studies in Mathematics and its Applications, 1988
^Ciarlet, P.G., Mathematical Elasticity, Vol. III: Theory of Shells, North-Holland, Amsterdam, Collection "Studies in Mathematics and its Applications", 2000
