Diiusive Bgk Approximations for Nonlinear Multidimensional Parabolic Equations

Discrete approximations for singularly perturbed boundary value problems with parabolic layers

REPORTRAPPORT Discrete approximations for singularly perturbed boundary value problems with parabolic layers Abstract Singularly perturbed boundary value problems for equations of elliptic and parabolic type are studied. For small values of the perturbation parameter, parabolic boundary layers appear in these problems. If classical discretisation methods are used, the solution of the nite diier...

Convergence of Diffusive Bgk Approximations for Nonlinear Strongly Parabolic Systems

On the Convergence of Discrete Kinetic Approximations to Hydrodynamic Equations

Introduction Motivations This thesis is devoted to present some new results in the theory of the semilinear approximations to hydrodynamic equations. More specically, the main purpose of this investigation is to prove the convergence of a class of discrete kinetic approximations , the BGK models, to some hyperbolic and hyperbolic-parabolic systems. These BGK models were introduced by Bathnagar,...

Topological and "–entropy for Large Volume Limits of Discretised Parabolic Equations

We consider semi-discrete and fully discrete approximations of nonlinear parabolic equations in the limit of unbounded domains, which by a scaling argument is equivalent to the limit of small viscosity. We define the spatial density of "–entropy, topological entropy and dimension for the attractors and show that these quantities are bounded. We also provide practical means of computing lower bo...

Explicit diffusive kinetic schemes for nonlinear degenerate parabolic systems

We design numerical schemes for nonlinear degenerate parabolic systems with possibly dominant convection. These schemes are based on discrete BGK models where both characteristic velocities and the source-term depend singularly on the relaxation parameter. General stability conditions are derived, and convergence is proved to the entropy solutions for scalar equations.