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Foreword

Pironneau Olivier — 2011

ESAIM: Mathematical Modelling and Numerical Analysis

Programming is an area at the interface between scientific computing and applied mathematics which has been very active lately and so it was thought that M2AN should open its pages to it in a special issue. This is because many new tools have appeared ranging from templates in C++ to Java interface library and parallel computing tools. There has been a diffusion of computer sciences into numerical analysis and these new tools have made possible the implementation of very complex methods such as...

Foreword

Olivier Pironneau — 2002

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Control of transonic shock positions

Olivier Pironneau — 2002

ESAIM: Control, Optimisation and Calculus of Variations

We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .

Control of Transonic Shock Positions

Olivier Pironneau — 2010

ESAIM: Control, Optimisation and Calculus of Variations

We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .

Coupling Darcy and Stokes equations for porous media with cracks

Christine BernardiFrédéric HechtOlivier Pironneau — 2005

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In order to handle the flow of a viscous incompressible fluid in a porous medium with cracks, the thickness of which cannot be neglected, we consider a model which couples the Darcy equations in the medium with the Stokes equations in the cracks by a new boundary condition at the interface, namely the continuity of the pressure. We prove that this model admits a unique solution and propose a mixed formulation of it. Relying on this formulation, we describe a finite element discretization and derive...

Coupling Darcy and Stokes equations for porous media with cracks

Christine BernardiFrédéric HechtOlivier Pironneau — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

In order to handle the flow of a viscous incompressible fluid in a porous medium with cracks, the thickness of which cannot be neglected, we consider a model which couples the Darcy equations in the medium with the Stokes equations in the cracks by a new boundary condition at the interface, namely the continuity of the pressure. We prove that this model admits a unique solution and propose a mixed formulation of it. Relying on this formulation, we describe a finite element discretization and derive...

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