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Dissertation
Nichtüberlappende Gebietszerlegungsmethoden für lineare und quasilineare (monotone und nichtmonotone) Probleme
(2009-12-15)
In dieser Arbeit werden nichtüberlappende Gebietszerlegungsmethoden einerseits hinsichtlich der zu lösenden Problemklassen verallgemeinert und andererseits in bisher nicht untersuchten Kontexten betrachtet. Dabei stehen funktionalanalytische Untersuchungen zur Wohldefiniertheit, eindeutigen Lösbarkeit und Konvergenz im Vordergrund.
Im ersten Teil werden lineare elliptische Dirichlet-Randwertprobleme behandelt, wobei neben Problemen mit dominantem Hauptteil auch solche mit singulärer Störung desselben, wie konvektions- ...
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 ...
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Evaluation von SINUS-Hessen 2005 - 2007
(2009-10-29)
Unter dem Namen SINUS werden seit über 10 Jahren bundesweit erfolgreiche Projekte zur Weiterentwicklung des mathematisch-naturwissenschaftlichen Unterrichts durchgeführt.
Das Projekt SINUS-Quest, dessen Abschlussbericht hier vorgelegt wird, entstand aus dem Anliegen der Projektleitung von SINUS-Hessen, eine eigene Evaluation des hessischen Projektes SINUS-Transfer (2005 – 2007) durchzuführen. Die Evaluation sollte nicht nur summativ sein, sondern den SINUS-Prozess selber mit beeinflussen. Dazu sollten schulspezifische ...
Preprint
Solution properties of the de Branges differential recurrence equation
(2005)
In this 1984 proof of the Bieberbach and Milin conjectures de Branges used a positivity result of special functions which follows from an identity about Jacobi polynomial sums thas was published by Askey and Gasper in 1976. The de Branges functions Tn/k(t) are defined as the solutions of a system of differential recurrence equations with suitably given initial values. The essential fact used in the proof of the Bieberbach and Milin conjectures is the statement Tn/k(t)<=0. In 1991 Weinstein presented another proof of ...
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
A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it
(2005)
In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.