120111067
Störungsrechnung für lineare gewöhnliche Differentialoperatoren Teil I
Es wird auf direktem Wege gezeigt, das alle nach Potenzen des Storparameters e fortschreitenden Reihen, die ein Eigenwertproblem, bestehend aus einem System linearer gestorter Differentialgleichungen und Randbedingungen, formal erfullen, auch konvergieren und das Problem losen. 
 
 
 
It is shown by a direct method that any series expansion in powers of the perturbation parameter e that formally satisfies an eigenvalue problem (system of linear disturbed differential equations and boundary conditions) does converge and solve the problem.
120742694
Uber adjungierte Systeme linearer Differentialgleichungen
120978454
Computation of Three Dimensional Dendrites with Finite Elements
Starting from an initial seed crystal inside an undercooled liquid, the solid phase begins to grow rapidly and develops unstable growth patterns. Some growth directions are preferred because of anisotropic parameters in the physical model. This results in the development of dendrites. The physical model includes the heat equation for both the liquid and solid phases; the GibbsÂ?Thomson law couples velocity and curvature of the interface and the temperature. We describe a numerical method that enables us to compute dendritic growth of crystals in two and three space dimensions. The method consists of two coupled finite element algorithms. The first one solves the heat equation; the other operates on a discretization of the free boundary and computes the evolution of this moving interface. The two methods work with totally independent grids. By using timedependent, locally refined and coarsened adaptive meshes in both methods, we are able to reach a spatial resolution necessary to compute dendritic growth in two and three space dimensions.
12266500
Approximation of crystalline dendrite growth in two space dimensions.
The phase transition between solid and liquid in an undercooled liquid leads to dendritic growth of the solid phase. The problem is modelled by the Stefan problem with a modified Gibbs-Thomson law, which includes the anisotropic mean curvature corresponding to a surface energy that depends on the direction of the interface normal. A finite element method for discretization of the Stefan problem is described which is based on a weak formulation of the anisotropic mean curvature flow. Numerical experiments with a nearly crystalline anisotropy are presented.