Lattice Boltzmann schemes rely on the enlargement of size target problem in order to solve PDEs a highly parallelizable and efficient kinetic-like fashion, split into collision stream phase. This structure, despite well-known advantages from computational standpoint, is not suitable construct rigorous notion consistency with respect equations provide precise stability. In alleviate these shorta...

We focus on mono-dimensional hyperbolic systems approximated by a particular lattice Boltzmann scheme. The scheme is described in the framework of the multiple relaxation times method and stability conditions are given. An analysis is done to link the scheme with an explicit finite differences approximation of the relaxation method proposed by Jin and Xin. Several numerical illustrations are gi...

In this talk we consider the finite element discretization of the Immersed Boundary Method (IBM) introduced by Peskin [6] for fluid-structure interaction problems. With respect to the original finite differences discretization the finite element approach can take advantage from the variational formulation in handling the Dirac delta function which takes into account the presence of the structur...