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Preprint
A generalization of Student’s t-distribution from the viewpoint of special functions
(2005)
Student’s t-distribution has found various applications in mathematical statistics. One of the main properties of the t-distribution is to converge to the normal distribution as the number of samples tends to infinity. In this paper, by using a Cauchy integral we introduce a generalization of the t-distribution function with four free parameters and show that it converges to the normal distribution again. We provide a comprehensive treatment of mathematical properties of this new distribution. Moreover, since the ...
Preprint
Artificial boundary conditions for the Stokes and Navier-Stokes equations in domains that are layer-like at infinity
(Universität Kassel, FB 17, Mathematik/Informatik, 2005)
Artificial boundary conditions are presented to approximate solutions to Stokes- and Navier-Stokes problems in domains that are layer-like at infinity. Based on results about existence and asymptotics of the solutions v^infinity, p^infinity to the problems in the unbounded domain Omega the error v^infinity - v^R, p^infinity - p^R is estimated in H^1(Omega_R) and L^2(Omega_R), respectively. Here v^R, p^R are the approximating solutions on the truncated domain Omega_R, the parameter R controls the exhausting of Omega. ...
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 ...
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
Existence of parameterized BV-solutions for rate-independent systems with discontinuous loads
(2019-09-25)
We study a rate-independent system with non-convex energy and in the case of a time-discontinuous loading. We prove existence of the rate-dependent viscous regularization by time-incremental problems, while the existence of the so called parameterized BV-solutions is obtained via vanishing viscosity in a suitable parameterized setting. In addition, we prove that the solution set is compact.
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 ...