Numerical analysis of Cauchy-type problem arising in electrical engineering

Inverse problems arise often in physical and technical processes. In this dissertation we consider problems of Cauchy-type based on the application of hybrid insulation. The experimental setup takes place at the NTNU Trondheim which placed at the disposal the measurements for the calculation. In this case we search Dirichlet or Neumann control for given Neumann measurements. After describing the problem of hybrid insulation and introducing the basic principals of functional analysis we analyse Nitsche's method for dealing with Dirichlet boundary conditions. The error estimates will be deduced and verified. Subsequent we give an introduction to inverse problems and their regularisation. We formulate three optimal control problems on the unit square based on the application of hybrid insulation. For given Neumann measurement we search Dirichlet control. For the regularisation we draw on three matrices. For all three problems we do numerical calculations with different grid refinements, different numbers of degrees of freedom on the boundary of control and different regularisation parameters. After comparison of the results within each problem we compare the results to each other. Based on these results we do the numerical caluclations for the application of hybrid insulation for searched Neumann control and given Neumann measurements.