We consider the positivity preserving property of first and higher order finite volume schemes
for one and two dimensional Euler equations of gas dynamics. A general framework is …

We prove convergence of the discontinuous Galerkin finite element method with
polynomials of arbitrary degree q≥ 0 on general unstructured meshes for scalar …

We consider a simple model case of stiff source terms in hyperbolic conservation laws,
namely, the case of scalar conservation laws with a zeroth order source with low regularity. It …

We prove a posteriori error estimates for a finite element method for systems of strictly
hyperbolic conservation laws in one space dimension, and design corresponding adaptive …

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 …

We establish the convergence of the finite volume method applied to multidimensional
hyperbolic conservation laws and based on monotone numerical flux-functions. Our …

In this paper, new a posteriors error estimates for the shock-capturing streamline diffusion
(SCSD) method and the shock-capturing discontinuous galerkin (SCDG) method for scalar …

In this paper, an ${L^\infty}({L^ 1}) $-error estimate for a class of finite volume methods for
the approximation of scalar multidimensional conservation laws is obtained. These methods …

Convergence and error estimates in finite volume schemes for general multidimensional scalar
conservation laws. I. Explicite mon Page 1 M2AN - MODÉLISATION MATHÉMATIQUE ET ANALYSE …

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 …