Philippe G. Ciarlet (born 14 October 1938) is a French mathematician, known particularly for his work on mathematical analysis of the finite element method.
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.
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.
[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.