Vanishing non-local regularization of a scalar conservation law.
Variational data assimilation for discrete Burgers equation.
Variational methods in nonlinear problems
Variational particle schemes for the porous medium equation and for the system of isentropic Euler equations
Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework of optimal transport theory. By discretizing these variational characterizations instead of the partial differential equations themselves, we obtain new schemes with remarkable stability properties. We show that they capture successfully the nonlinear features of the flows, such as shocks and rarefaction waves for...
Vertex centred Discretization of Two-Phase Darcy flows on General Meshes
This paper concerns the discretization of multiphase Darcy flows, in the case of heterogeneous anisotropic porous media and general 3D meshes used in practice to represent reservoir and basin geometries. An unconditionally coercive and symmetric vertex centred approach is introduced in this paper. This scheme extends the Vertex Approximate Gradient scheme (VAG), already introduced for single phase diffusive problems in [9], to multiphase Darcy flows....
Vibrations of a beam between obstacles. Convergence of a fully discretized approximation
We consider mathematical models describing dynamics of an elastic beam which is clamped at its left end to a vibrating support and which can move freely at its right end between two rigid obstacles. We model the contact with Signorini's complementary conditions between the displacement and the shear stress. For this infinite dimensional contact problem, we propose a family of fully discretized approximations and their convergence is proved. Moreover some examples of implementation are presented....
Viscosity solutions and standard Riemann semigroup for conservation laws with boundary
Viscous approach for Linear Hyperbolic Systems with Discontinuous Coefficients
We introduce small viscosity solutions of hyperbolic systems with discontinuous coefficients accross the fixed noncharacteristic hypersurface Under a geometric stability assumption, our first result is obtained, in the multi-D framework, for piecewise smooth coefficients. For our second result, the considered operator is with (expansive case not included in our first result), thus resulting in an infinity of weak solutions. Proving that this problem is uniformly Evans-stable, we show that...
Viscous profiles for traveling waves of scalar balance laws: The uniformly hyperbolic case.
Vitesse de convergence vers le réel des résonances