Optimization and control theory
Works on the approximation of the Riccati equation
Results on duality in optimization and variational inequalities
Finite element methods
Introduction of two families of edge and face finite element
in two and three space dimension
Application to Stokes and Maxwell equations and to plate problems
Coupling between finite element and integral equations.
Integral equations
Introduction of coercive variational formulations and
approximations using finite element
Application to:
- Laplace Equation and simple layer potential
- Eddy currents
- Stokes Equation and elastic problems
Introduction of coercive variational formulations to treat
the hyper singular kernels in the following case:
- Laplace Equation and double layer potential
- Helmholtz Equation
- Elastic waves equation
- Piezo-elastic waves devices
Non linear hyperbolic equations
Result of existence and uniqueness for a first order equation
with boundary conditions
Theoretical results and numerical techniques for
Maxwell equations in electromagnetic problems
Study of integral equations. Use of the Helmholtz decomposition
Study of approximated boundary conditions
Study of chiral media
Study of diffraction by arrays
Low frequency analysis
Resonant frequencies in a grating
Preconditionners