TY - GEN A1 - Weiser, Martin A1 - Gänzler, Tobias A1 - Schiela, Anton T1 - A Control Reduced Primal Interior Point Method for PDE Constrained Optimization N2 - A primal interior point method for control constrained optimal control problems with PDE constraints is considered. Pointwise elimination of the control leads to a homotopy in the remaining state and dual variables, which is addressed by a short step pathfollowing method. The algorithm is applied to the continuous, infinite dimensional problem, where discretization is performed only in the innermost loop when solving linear equations. The a priori elimination of the least regular control permits to obtain the required accuracy with comparable coarse meshes. Convergence of the method and discretization errors are studied, and the method is illustrated at two numerical examples. T3 - ZIB-Report - 04-38 KW - interior point methods in function space KW - optimal control KW - finite elements KW - discretization error Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8138 ER - TY - GEN A1 - Weiser, Martin T1 - Pointwise Nonlinear Scaling for Reaction-Diffusion-Equations N2 - Parabolic reaction-diffusion systems may develop sharp moving reaction fronts which pose a challenge even for adaptive finite element methods. We propose a method to transform the equation into an equivalent form that usually exhibits solutions which are easier to discretize, giving higher accuracy for a given number of degrees of freedom. The transformation is realized as an efficiently computable pointwise nonlinear scaling that is optimized for prototypical planar travelling wave solutions of the underlying reaction-diffusion equation. The gain in either performance or accuracy is demonstrated on different numerical examples. T3 - ZIB-Report - 07-45 KW - reaction-diffusion equations KW - travelling waves KW - nonlinear scaling KW - discretization error Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10493 SN - 1438-0064 ER -