Section: Overall Objectives
Development of the modular C++-library Concha
This library is the fundamental tool for our work on numerical simulations. It is designed in such a way that the implementation and testing of new algorithms in such different fields as hyperbolic equations and viscoelastic flows can be done with a minimum amount of work. It has been shown that our preliminary code for the Giesekus model of polymer flows has advantages over the commercial code PolyFlow® with respect to computing time and robustness. For more details see Section 5.1 .
Habilitation thesis of Robert Luce
Robert Luce has defended his habilitation thesis on the subject of a new class of finite elements on general quadrilateral and hexahedral meshes, called 'pseudo-conforming'  .
Quasi-optimality of adaptive finite elements
We have extended convergence results with complexity estimates to mixed and nonconforming finite element discretizations, as well as to finite elements on quadrilateral meshes and the Stokes equations. Our approach is based on a new adaptive marking strategy, and the proofs required the development of new techniques, such as a reduction property of the error estimator under local refinement and a complexity estimate for meshes with hanging nodes, see Section 6.1 for more details. These theoretical results are expected to provide insight necessary for the improvement of practical algorithms.