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Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition

Eliane Bécache, Jeronimo Rodríguez, Chrysoula Tsogka (2009)

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

The problem of modeling acoustic waves scattered by an object with Neumann boundary condition is considered. The boundary condition is taken into account by means of the fictitious domain method, yielding a first order in time mixed variational formulation for the problem. The resulting system is discretized with two families of mixed finite elements that are compatible with mass lumping. We present numerical results illustrating that the Neumann boundary condition on the object is not always correctly...

Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition

Eliane Bécache, Jeronimo Rodríguez, Chrysoula Tsogka (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

The problem of modeling acoustic waves scattered by an object with Neumann boundary condition is considered. The boundary condition is taken into account by means of the fictitious domain method, yielding a first order in time mixed variational formulation for the problem. The resulting system is discretized with two families of mixed finite elements that are compatible with mass lumping. We present numerical results illustrating that the Neumann boundary condition on the object is not always...

Convergent finite element discretizations of the Navier-Stokes-Nernst-Planck-Poisson system

Andreas Prohl, Markus Schmuck (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose and analyse two convergent fully discrete schemes to solve the incompressible Navier-Stokes-Nernst-Planck-Poisson system. The first scheme converges to weak solutions satisfying an energy and an entropy dissipation law. The second scheme uses Chorin's projection method to obtain an efficient approximation that converges to strong solutions at optimal rates.

Couches limites semilinéaires

Franck Sueur (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

On s’intéresse à des problèmes mixtes pour des systèmes symétriques hyperboliques multidimensionnels semilinéaires perturbés par une petite viscosité. La description à la limite non visqueuse recquiert des développements du type BKW mettant en évidence une couche limite caractéristique (CLC) et une couche limite non caractéristique (CLNC). Ce thème traité dans [12] est ici enrichi de trois améliorations :l’étude inclut des développements ayant peu de termes (comme un seul terme),on étudie aussi...

Counterexamples to the Strichartz inequalities for the wave equation in general domains with boundary

Oana Ivanovici (2012)

Journal of the European Mathematical Society

In this paper we consider a smooth and bounded domain Ω ⊂ ℝ d of dimension d ≥ 2 with boundary and we construct sequences of solutions to the wave equation with Dirichlet boundary condition which contradict the Strichartz estimates of the free space, providing losses of derivatives at least for a subset of the usual range of indices. This is due to microlocal phenomena such as caustics generated in arbitrarily small time near the boundary. Moreover, the result holds for microlocally strictly convex domains...

Critical phenomena in gravitational collapse

Carsten Gundlach (1997)

Banach Center Publications

A mini-introduction to critical phenomena in gravitational collapse is combined with a more detailed discussion of how gravity regularizes the 'critical spacetimes' that dominate these phenomena.

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