Philippe G. Ciarlet

Last updated
Philippe Ciarlet
Born14 October 1938
Paris, France
Alma mater École polytechnique
Awards Légion d'honneur
Scientific career
Fields Mathematics
Institutions Pierre and Marie Curie University
City University of Hong Kong
Doctoral advisor Richard S. Varga

Philippe G. Ciarlet (born 14 October 1938) is a French mathematician, known particularly for his work on mathematical analysis of the finite element method. He has contributed also to elasticity, to the theory of plates and shells and differential geometry.

Contents

Biography

Philippe Ciarlet is a former student of the École Polytechnique and the École des ponts et chaussées. He completed his PhD at Case Institute of Technology in Cleveland in 1966 under the supervision of Richard S. Varga. He also holds a doctorate in mathematical sciences from the Faculty of Sciences of Paris (doctorate under the supervision of Jacques-Louis Lions in 1971).

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.

He is Professor Emeritus at the University of Hong Kong, Professor at the City University of Hong Kong, [1] [2] Member of the Academy of Technology [3] in 1989, Member of the French Academy of Sciences since 1991 (in the Mechanical and Computer Sciences section), [4] Member of the Indian Academy of Sciences in 2001, Member of the European Academy of Sciences in 2003, Member of the World Academy of Sciences in 2007, Member of the Chinese Academy of Sciences in 2009, Member of the American Mathematical Society since 2012, [5] and Member of the Hong-Kong Academy of Sciences in 2015.

Scientific work

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]

Honours and awards

National Order of the Legion of Honour of France:

Member or Foreign Member of the following Academies :

Prizes

Academic awards

Related Research Articles

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References

  1. ↑ "Académie des sciences de Hong Kong".
  2. ↑ "Université de Hong Kong".
  3. ↑ "Académie des technologies". Archived from the original on 2019-04-15. Retrieved 2019-07-17.
  4. ↑ "Académie des sciences".
  5. ↑ "American Mathematical Society".
  6. ↑ 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
  7. ↑ Ciarlet, P.G., « Discrete variational Green’s function. I », Aequationes Math., 4 (1970), p. 74–82
  8. ↑ Ciarlet, P.G., « Discrete maximum principe for finite-difference operators », Aequationes Math., 4 (1970), p. 338–352
  9. ↑ 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
  10. 1 2 a et b Ciarlet, P.G., The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, Mathematics and its Applications, 1978
  11. ↑ Ciarlet, P.G.; Destuynder P., « A justification of the two-dimensional linear plate model », J. Mécanique, 18 (1979), p. 315–344
  12. ↑ 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
  13. ↑ Ciarlet, P.G., « A justification of the von Kármán equations », Arch. RationalMech. Anal., 73 (1980), p. 349–389
  14. ↑ 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
  15. ↑ Ciarlet, P.G., Plates and Junctions in Elastic Multi-Structures : An Asymptotic Analysis, Paris et Heidelberg, Masson & Springer-Verlag, 1990
  16. ↑ Bernadou, M.; Ciarlet, P.G.; Miara, B., « Existence theorems for two-dimensional linear shell theories », J. Elasticity, 34 (1994), p. 111–138
  17. ↑ 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
  18. ↑ 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
  19. ↑ Ciarlet P.G.; Lods, V., « Asymptotic analysis of linearly elastic shells : "Generalized membrane shells" », J. Elasticity, 43 (1996), p. 147–188
  20. ↑ 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
  21. ↑ Ciarlet, P.G.; Neˇ Cas, J., « Injectivity and self-contact in nonlinear elasticity », Arch. Rational Mech. Anal., 97 (1987), p. 171–188
  22. ↑ 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
  23. ↑ Ciarlet, P.G.; Gratie, L.; Mardare C., « A nonlinear Korn inequality on a surface », J. Math. Pures Appl., 85 (2006), p. 2-16
  24. ↑ 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
  25. ↑ Ciarlet, P.G.; Ciarlet, JR., P., « Direct computation of stresses in planar linearized elasticity », Math. Models Methods Appl. Sci., 19 (2009), p. 1043-1064
  26. ↑ Ciarlet, P.G.; Mardare, C., « Existence theorems in intrinsic nonlinear elasticity », J. Math. Pures Appl., 94 (2010), p. 229-243
  27. ↑ Ciarlet, P.G., Introduction à l’Analyse Numérique Matricielle et à l’Optimisation, Paris, Masson, 1982
  28. ↑ Ciarlet, P.G., An Introduction to Differential Geometry, with Applications to Elasticity, Dordrecht, Springer, 2005
  29. ↑ Ciarlet, P.G., Linear and Nonlinear Functional Analysis with Applications, Philadelphia, SIAM, 2013
  30. ↑ Ciarlet, P.G.; Rabier, P., Les équations de von Kármán, Lectures Notes in Mathematics, Vol.826, Berlin, Springer-Verlag, 1980
  31. ↑ Ciarlet, P.G., Mathematical Elasticity, Vol. I : Three-Dimensional Elasticity, North-Holland, Amsterdam, Series "Studies in Mathematics and its Applications, 1988
  32. ↑ Ciarlet, P.G., Mathematical Elasticity, Vol. II: Theory of Plates, North-Holland, Amsterdam, Series "Studies in Mathematics and its Applications, 1988
  33. ↑ Ciarlet, P.G., Mathematical Elasticity, Vol. III: Theory of Shells, North-Holland, Amsterdam, Collection "Studies in Mathematics and its Applications", 2000
  34. ↑ "Académie des sciences".
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