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- Michael Junk, Axel Klar, Li-Shi Luo
- 2005
In this article we analyze the lattice Boltzmann equation (LBE) by using the asymptotic expansion technique. We first relate the LBE to the finite discrete-velocity model (FDVM) of the Boltzmann… (More)
- A. Aw, Axel Klar, Michel Rascle, Thorsten Materne
- SIAM Journal of Applied Mathematics
- 2002
In this paper we establish a connection between a microscopic follow-the-leader model based on ordinary differential equations and a semidiscretization of a macroscopic continuum model based on a… (More)
- Mapundi K. Banda, Michael Herty, Axel Klar
- NHM
- 2006
We investigate coupling conditions for gas transport in networks where the governing equations are the isothermal Euler equations. We discuss intersections of pipes by considering solutions to… (More)
- Axel Klar, Raimund Wegener
- SIAM Journal of Applied Mathematics
- 1998
In the present paper multilane models for vehicular traac are considered. A microscopic multilane model based on reaction thresholds is developed. Based on this model an Enskog like kinetic model is… (More)
- Mapundi K. Banda, Michael Herty, Axel Klar
- NHM
- 2006
- Axel Klar
- 2007
An asymptotic-induced scheme for nonstationary transport equations with the diiu-sion scaling is developed. The scheme works uniformly for all ranges of mean free paths. It is based on the asymptotic… (More)
- Axel Klar, Raimund Wegener
- SIAM Journal of Applied Mathematics
- 2000
- Michael Herty, Axel Klar, Benedetto Piccoli
- SIAM J. Math. Analysis
- 2007
We consider a model for supply chains governed by partial differential equations. The mathematical properties of a continuous model are discussed and existence and uniqueness is proven. Moreover,… (More)
- Axel Klar
- SIAM J. Scientific Computing
- 1998
This paper deals with domain decomposition methods for kinetic and drift diiusion semiconductor equations. In particular accurate coupling conditions at the interface between the kinetic and drift… (More)
- Axel Klar, Raimund Wegener
- SIAM Journal of Applied Mathematics
- 1998
In this paper the work presented in 4] is continued. The present paper contains detailed numerical investigations of the models developed there. A numerical method to treat the kinetic equations… (More)