Redaktion: K. Sigmund, G. Greschonig (Univ. Wien, Strudlhofgasse ...

154 Numerische Mathematik, Wissenschaftliches Rechnen
and below up to multiplicative constants that do neither depend on the meshsize
nor on the plate’s thickness and are uniform for a wide range of stabilisation
parameter. The error is controlled in norms that are known to converge to zero in
a quasi-optimal way.
[1] C. Carstensen, J. Schöberl: Residual-Based A Posteriori Error Estimate for
a Mixed Reissner-Mindlin Plate Finite Element Method. SFB-Report No.
00-31, Johannes Kepler Universität Linz, SFBF013, Linz, Austria
The Numerics of Nonlinear Parabolic Problems
MECHTHILD THALHAMMER
(gemeinsam mit Alexander Ostermann)
Department of Engineering Mathematics, Geometry and Computer Science,
Univ. of Innsbruck, Technikerstraße 13, 6020 Innsbruck
Mechthild.Thalhammer@uibk.ac.at
http://techmath.uibk.ac.at/mathematik/thalhammer/
We consider fully nonlinear initial-boundary value problems of parabolic type
modelling for example nonlinear diffusion or heat conduction processes. When
we apply a numerical method for discretizing such a problem in time, a matter
of interest is whether the discretization reproduces the trajectories and whether it
captures the dynamics of the underlying problem correctly.
For the analysis, we write the partial differential equation as abstract ordinary differential
equation, and we work in the framework of analytic semigroups and Banach
space valued Hölder continuous functions. For the classes of implicit Runge-
Kutta and linear multistep methods we show that the quantitative and qualitative
properties of the original problem are well preserved.
Simulation of the Dynamics of Tethered Satellite Systems
HANS TROGER
(gemeinsam mit M.Matzl, W.Poth, A.Steindl, G.Wiedermann)
Institut für Mechanik, TU Wien
Hans.Troger@tuwien.ac.at
http://mch2ws2.mechanik.tuwien.ac.at/˜htroger
The dynamics of tethered satellite systems, that is an arrangement of two or more
satellites, which are connected by thin long cables in orbit around a planet, is described
by a coupled set of nonlinear ordinary and partial differential equations.
We present the equations in weak form, which for the system of varying mass
composition is nontrivial. Since the equations are stiff their numerical treatment
requires special measures. One possibility is to introduce an alternative set of
variables (natural string variables) for the description of the deformation of the