27 citations · 67 across the 6 of their papers we have counts for
7 papers
Concentration of measure-valued solutions for semilinear parabolic equations
Charlie Lebarbé, Émilien Flayac, Michel Fournié +2
The moment-sum-of-squares hierarchy provides a powerful framework for solving non-convex optimal control problems by constructing a sequence of convex semidefinite relaxations. How…
Discretization of the Burgers' equation as a port-Hamiltonian system
Lorenzo Agostini, Michel Fournié, Ghislain Haine
The numerical simulation of the inviscid Burgers' equation is often hindered by spurious oscillations near discontinuities. To mitigate this issue, a viscous term can be introduced…
Stability and optimal convergence of unfitted extended finite element methods with Lagrange multipliers for the Stokes equations
Michel Fournié, Alexei Lozinski
We study a fictitious domain approach with Lagrange multipliers to discretize Stokes equations on a mesh that does not fit the boundaries. A mixed finite element method is used for…
High-order ADI schemes for convection-diffusion equations with mixed derivative terms
Bertram Düring, Michel Fournié, Alain Rigal
We present new high-order Alternating Direction Implicit (ADI) schemes for the numerical solution of initial-boundary value problems for convection-diffusion equations with mixed d…
A fictitious domain finite element method for simulations of fluid-structure interactions: The Navier-Stokes equations coupled with a moving solid
Sébastien Court, Michel Fournié
The paper extends a stabilized fictitious domain finite element method initially developed for the Stokes problem to the incompressible Navier-Stokes equations coupled with a movin…
A fictitious domain approach for Fluid-Structure Interactions based on the eXtended Finite Element Method
Sébastien Court, Michel Fournié, Alexei Lozinski
In this work we develop a fictitious domain method for the Stokes problem which allows computations in domains whose boundaries do not depend on the mesh. The method is based on th…
A fictitious domain approach for the Stokes problem based on the extended finite element method
Sébastien Court, Michel Fournié, Alexei Lozinski
In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard].…