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. His contributions and those of his collaborators can be found in his well-known book.