Discretisation and Solver Methods for a Model for Solid-Gas-Phase of a Crystal Growth Apparatus.

Juergen Geiser

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 37 pp.

MSC 2000

49J20 Optimal control problems involving partial differential equations

76M10 Finite element methods

Abstract
We present discretisation and solver methods for a model for a solid-gas phase of a crystal growth aparatus. The model-equations are coupled Eulerian- and Heat-transfer-equations with flux-boundary conditions. For more detailed discussion we consider simpler equations and present time- and space-decomposition methods as a solver methods to decouple the multi-physics processes. We present the error-analysis for the discretisation methods and solver methods. Numerical expeeriments are done for the eulerian- and heat-transfer-equation with decomposition methods. We present a real-life application of a crystal growth apparatus, based on the underlying stationary heat conduction. Finally we discuss the further works in the error-analysis and the application to a more complex model of crystal growth.