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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 ...
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.
Preprint
An algebraic proof of Iitaka's conjecture C2,1
(Universität Kassel, FB 17, Mathematik/Informatik, 2002)
We give a proof of Iitaka's conjecture C2,1 using only elementary methods from algebraic geometry.
Preprint
Rekonstruktive Videoanalyse
(2009-03-23)
Der Artikel stellt wahrnehmungs- und interaktionstheoretische Grundlagen einer rekonstruktiven Videoanalyse dar. Entgegen alltagsweltlicher Abbildungstheorien wird aufgezeigt, dass Bilderstellung und Bildgebrauch sozial situierte Praktiken sind, die bei einer Analyse zu berücksichtigen sind. Praktisches Vorgehen und Anwendungen im Bereich der Sozialen Arbeit werden dargelegt.
Preprint
Preconditioner updates applied to CFD model problems
(2007)
In the present paper we concentrate on solving sequences of nonsymmetric linear systems with block structure arising from compressible flow problems. We attempt to improve the solution process by sharing part of the computational effort throughout the sequence. This is achieved by application of a cheap updating technique for preconditioners which we adapted in order to be used for our applications. Tested on three benchmark compressible flow problems, the strategy speeds up the entire computation with an acceleration ...
Preprint
The Navier-Stokes Equations with Particle Methods
(2007)
The non-stationary nonlinear Navier-Stokes equations describe the motion of a viscous incompressible fluid flow for 0<t≤T in some bounded three-dimensional domain.
Up to now it is not known wether these equations are well-posed or not. Therefore we use a particle method to develop a system of approximate equations. We show that this system can be solved uniquely and globally in time and that its solution has a high degree of spatial regularity. Moreover we prove that the system of approximate solutions has an ...
Preprint
Lagrangian approximations and weak solutions of the Navier-Stokes equations
(2007)
The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian representation of the flow, where the latter is defined by the trajectories of the particles of the fluid. The method leads to ...