TY - GEN A1 - Schiela, Anton A1 - Günther, Andreas T1 - Interior Point Methods in Function Space for State Constraints - Inexact Newton and Adaptivity N2 - We consider an interior point method in function space for PDE constrained optimal control problems with state constraints. Our emphasis is on the construction and analysis of an algorithm that integrates a Newton path-following method with adaptive grid refinement. This is done in the framework of inexact Newton methods in function space, where the discretization error of each Newton step is controlled by adaptive grid refinement in the innermost loop. This allows to perform most of the required Newton steps on coarse grids, such that the overall computational time is dominated by the last few steps. For this purpose we propose an a-posteriori error estimator for a problem suited norm. T3 - ZIB-Report - 09-01 KW - interior point methods KW - function space KW - adaptivity KW - state constraints Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11007 SN - 1438-0064 ER - TY - GEN A1 - Günther, Andreas A1 - Lamecker, Hans A1 - Weiser, Martin T1 - Direct LDDMM of Discrete Currents with Adaptive Finite Elements N2 - We consider Large Deformation Diffeomorphic Metric Mapping of general $m$-currents. After stating an optimization algorithm in the function space of admissable morph generating velocity fields, two innovative aspects in this framework are presented and numerically investigated: First, we spatially discretize the velocity field with conforming adaptive finite elements and discuss advantages of this new approach. Second, we directly compute the temporal evolution of discrete $m$-current attributes. T3 - ZIB-Report - 11-22 KW - Large Deformation KW - Diffeomorphic Registration KW - Matching KW - Currents KW - Adaptive Finite Elements Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-13090 ER -