This book introduces the basic ideas to build discontinuous Galerkin methods and, at the
same time, incorporates several recent mathematical developments. The presentation is to a …

We give an overview of recent developments concerning the use of adjoint methods in two
areas: the a posteriori error analysis of finite element methods for the numerical solution of …

The aim of this book is to present some mathematical results describing the transition from
kinetic theory, and, more precisely, from the Boltzmann equation for perfect gases to …

This paper presents a stabilization technique for approximating transport equations. The key
idea consists in introducing an artificial diffusion based on a two-level decomposition of the …

This paper is devoted to the mathematical definition of the extrapolation length which
appears in the diffusion approximation. To obtain this result, we describe the spectral …

Perturbations of Positive Semigroups with Applications is a self-contained introduction to
semigroup theory with emphasis on positive semigroups on Banach lattices and …

We propose stable variational formulations for certain linear, unsymmetric operators with first
order transport equations in bounded domains serving as the primary focus of this paper …

Cet ouvrage présente l'analyse mathématique de systèmes issus de l'industrie pétrolière. Le
lecteur y trouvera, avec une présentation d'ensemble du sujet et les rappels utiles à …

Measure solutions to the linear multi-dimensional transport equation with non-smooth
coefficients Page 1 COMMUN. IN PARTIAL DIFFERENTIAL EQUATIONS, 22(1&2), 337-358 …

We consider the {a posteriori} error analysis of hp-discontinuous Galerkin finite element
approximations to first-order hyperbolic problems. In particular, we discuss the question of …