This paper deal with designing of weighted particle approximation of conservation laws.
New ideas concerning the use of variable smoothing length, renormalization and the use of …

This text presents a comprehensive mathematical theory for elliptic, parabolic, and
hyperbolic differential equations. It compares finite element and finite difference methods …

This paper is devoted to the study of the finite volume methods used in the discretization of
conservation laws defined on bounded domains. General assumptions are made on the …

This paper is devoted to the study of the convergence of weighted particle approximation of
nonlinear multidimensional conservation laws. For Euler equations the method is closely …

This paper is devoted to the study of a new kind of meshfree scheme based on a new class
of meshfree derivatives: the renormalized meshfree derivatives, which improve the …

We study the theoretical and numerical coupling of two general hyperbolic conservation
laws. The coupling preserves in a weak sense the continuity of the solution at the interface …

In this contribution we give an overview on recent progress in obtaining a posteriori error
control for finite volume and discontinuous Galerkin approximations of non‐linear hyperbolic …

This paper is the third of a series where the convergence analysis of SPH method for
multidimensional conservation laws is analyzed. In this paper, two original numerical …

We establish a convergence rate of the renormalized meshfree numerical scheme applied to
scalar conservation laws. Renormalization is a tool introduced in order to eliminate the …

The SPH method (Smooth Particle Hydrodynamics) is our starting point. It has been
“discovered” in 1977 by Lucy ([15]) a British astrophysicist. At this time his computation only …