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Preprint
Stability of preconditioned finite volume schemes at low Mach numbers
(Universität Kassel, FB 17, Mathematik/Informatik, 2004)
In [4], Guillard and Viozat propose a finite volume method for the simulation of inviscid steady as well as unsteady flows at low Mach numbers, based on a preconditioning technique. The scheme satisfies the results of a single scale asymptotic analysis in a discrete sense and comprises the advantage that this can be derived by a slight modification of the dissipation term within the numerical flux function. Unfortunately, it can be observed by numerical experiments that the preconditioned approach combined with an ...
Preprint
Anisotropic adaptive resolution of boundary layers for heat conduction problems
(Universität Kassel, FB 17, Mathematik/Informatik, 2005)
We deal with the numerical solution of heat conduction problems featuring steep gradients. In order to solve the associated partial differential equation a finite volume technique is used and unstructured grids are employed. A discrete maximum principle for triangulations of a Delaunay type is developed. To capture thin boundary layers incorporating steep gradients an anisotropic mesh adaptation technique is implemented. Computational tests are performed for an academic problem where the exact solution is known as ...
Preprint
An approximation method using approximate approximations
(Universität Kassel, FB 17, Mathematik/Informatik, 2005)
The aim of this paper is to extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present paper we develop an approximation procedure for the solution of the interior Dirichlet problem for the Laplace equation in two dimensions using approximate approximations. The procedure is based on potential ...
Aufsatz
B 6.2 Discussion-Summary by the Coordinator
(Athen, Hermann (Hrsg.), 1977)
Preprint
Exact algorithms for p-adic fields and epsilon constant conjectures
(2006)
We develop several algorithms for computations in Galois extensions of p-adic fields. Our algorithms are based on existing algorithms for number fields and are exact in the sense that we do not need to consider approximations to p-adic numbers. As an application we describe an algorithmic approach to prove or disprove various conjectures for local and global epsilon constants.