## Fachbereich Mathematik

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- On the Connection of the Formulae for Entropy and Stationary Distribution (1994)
- As it is well known in statistical physics the stationary distribution can be obtained by maximizing entropy. We show how one can reconstruct the formula for entropy knowing the formula for the stationary distribution. A general case is discussed and some concrete physical examples are considered.

- A Numerical Method for Computing Asymptotic States and Outgoing Distributions for Kinetic Linear Half-Space Problems (1994)
- Linear half-space problems can be used to solve domain decomposition problems between Boltzmann and aerodynamic equations. A new fast numerical method computing the asymptotic states and outgoing distributions for a linearized BGK half-space problem is presented. Relations with the so-called variational methods are discussed. In particular, we stress the connection between these methods and Chapman-Enskog type expansions.

- A kinetic model for vehicular traffic: Existence of stationary solutions (1998)
- In this paper the kinetic model for vehicular traffic developed in [3,4] is considered and theoretical results for the space homogeneous kinetic equation are presented. Existence and uniqueness results for the time dependent equation are stated. An investigation of the stationary equation leads to a boundary value problem for an ordinary differential equation. Existence of the solution and some properties are proved. A numerical investigation of the stationary equation is included.

- Discretizations for the Incompressible Navier-Stokes Equations based on the Lattice Boltzmann Method (1999)
- A discrete velocity model with spatial and velocity discretization based on a lattice Boltzmann method is considered in the low Mach number limit. A uniform numerical scheme for this model is investigated. In the limit, the scheme reduces to a finite difference scheme for the incompressible Navier-Stokes equation which is a projection method with a second order spatial discretization on a regular grid. The discretization is analyzed and the method is compared to Chorin's original spatial discretization. Numerical results supporting the analytical statements are presented.

- Convergence of Alternating Domain Decomposition Schemes for Kinetic and Aerodynamic Equations (1994)
- A domain decomposition scheme linking linearized kinetic and aerodynamic equations is considered. Convergence of the alternating scheme is shown. Moreover the physical correctness of the obtained coupled solutions is discussed.

- Domain Decomposition for Kinetic Problems with Nonequilibrium States (1994)
- A nonequilibrium situation governed by kinetic equations with strongly contrasted Knudsen numbers in different subdomains is discussed. We consider a domain decomposition problem for Boltzmann- and Euler equations, establish the correct coupling conditions and prove the validity of the obtained coupled solution. Moreover numerical examples comparing different types of coupling conditions are presented.

- Computation of Nonlinear Functionals in Particle Methods (1994)
- We consider the numerical computation of nonlinear functionals of distribution functions approximated by point measures. Two methods are described and estimates for the speed of convergence as the number of points tends to infinity are given. Moreover numerical results for the entropy functional are presented.

- Asymptotic-Induced Domain Decomposition Methods for Kinetic and Drift Diffusion Semiconductor Equations (1995)
- This paper deals with domain decomposition methods for kinetic and drift diffusion semiconductor equations. In particular accurate coupling conditions at the interface between the kinetic and drift diffusion domain are given. The cases of slight and strong nonequilibrium situations at the interface are considered and some numerical examples are shown.