A note on Poincar\'e- and Friedrichs-type inequalities

We introduce a simple criterion to check coercivity of bilinear forms on subspaces of Hilbert-spaces. The presented criterion allows to derive many standard and non-standard variants of Poincar\'e- and Friedrichs-type inequalities with very little effort

CRC 1114 - Report Membrane Deformation by N-BAR Proteins: Extraction of membrane geometry and protein diffusion characteristics from MD simulations

We describe simulations of Proteins and artificial pseudo-molecules interacting and shaping lipid bilayer membranes. We extract protein diffusion Parameters, membrane deformation profiles and the elastic properties of the used membrane models in preparation of calculations based on a large scale continuum model

Globalization of nonsmooth Newton methods for optimal control problems

We present a new approach for the globalization of the primal-dual active set or equivalently the nonsmooth Newton method applied to an optimal control problem. The basic result is the equivalence of this method to a nonsmooth Newton method applied to the nonlinear Schur complement of the optimality system. Our approach does not require the construction of an additional merit function or additional descent direction. The nonsmooth Newton directions are naturally appropriate descent directions for a smooth dual energy and guarantee global convergence if standard damping methods are applied

Nonsmooth Schur-Newton methods for nonsmooth saddle point problems.

We introduce and analyze nonsmooth Schur-Newton methods for a class of nonsmooth saddle point problems. The method is able to solve problems where the primal energy decomposes into a convex smooth part and a convex separable but nonsmooth part. The method is based on nonsmooth Newton techniques for an equivalent unconstrained dual problem. Using this we show that it is globally convergent even for inexact evaluation of the linear subproblems

A note on Poincaré- and Friedrichs-type inequalities

We introduce a simple criterion to check coercivity of bilinear forms on subspaces of Hilbert-spaces. The presented criterion allows to derive many standard and non-standard variants of Poincar\'e- and Friedrichs-type inequalities with very little effort

The dune-subgrid module and some applications

We present an extension module for the Dune system. This module, called dune-subgrid, allows to mark elements of another Dune hierarchical grid. The set of marked elements can then be accessed as a Dune grid in its own right. dune-subgrid is free software and is available for download (External Dune Modules: www.​dune-project.​org/​downloadext.​html). We describe the functionality and use of dune-subgrid, comment on its implementation, and give two example applications. First, we show how dune-subgrid can be used for micro-FE simulations of trabecular bone. Then we present an algorithm that allows to use exact residuals for the adaptive solution of the spatial problems of time-discretized evolution equations