A discontinuous Galerkin discretization for solving the two-dimensional gas dynamics equations written under total Lagrangian formulation on general unstructured grids. - François Vilar; Pierre-Henri Maire; Rémi Abgrall (J. Comput. Phys., 2014)

Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part I: The one-dimensional case. - François Vilar; Chi-Wang Shu; Pierre-Henri Maire (J. Comput. Phys., 2016)

Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part II: The two-dimensional case. - François Vilar; Chi-Wang Shu; Pierre-Henri Maire (J. Comput. Phys., 2016)

A posteriori correction of high-order discontinuous Galerkin scheme through subcell finite volume formulation and flux reconstruction. - François Vilar (J. Comput. Phys., 2019)

textit{A Posteriori} local subcell correction of high-order discontinuous Galerkin scheme for conservation laws on two-dimensional unstructured grids. - François Vilar; Rémi Abgrall (CoRR, 2022)

A posteriori Finite-Volume local subcell correction of high-order discontinuous Galerkin schemes for the nonlinear shallow-water equations. - Ali Haidar; Fabien Marche; François Vilar (J. Comput. Phys., 2022)

A Posteriori Local Subcell Correction of High-Order Discontinuous Galerkin Scheme for Conservation Laws on Two-Dimensional Unstructured Grids. - François Vilar; Rémi Abgrall (SIAM J. Sci. Comput., 2024)

Free-Boundary Problems for Wave-Structure Interactions in Shallow-Water: DG-ALE Description and Local Subcell Correction. - Ali Haidar; Fabien Marche; François Vilar (J. Sci. Comput., 2024)

Local subcell monolithic DG/FV convex property preserving scheme on unstructured grids and entropy consideration. - François Vilar (J. Comput. Phys., 2025)

An ALE Numerical Method for the Waterline Evolution of a Floating Object with Non-linear Shallow-water Equations. - Ali Haidar; Fabien Marche; François Vilar (J. Sci. Comput., 2025)