Browsing by Author "Rösel, Simon"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
- ItemDensity of convex intersections and applications(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Hintermüller, Michael; Rautenberg, Carlos N.; Rösel, SimonIn this paper we address density properties of intersections of convex sets in several function spaces. Using the concept of Gamma-convergence, it is shown in a general framework, how these density issues naturally arise from the regularization, discretization or dualization of constrained optimization problems and from perturbed variational inequalities. A variety of density results (and counterexamples) for pointwise constraints in Sobolev spaces are presented and the corresponding regularity requirements on the upper bound are identified. The results are further discussed in the context of finite element discretizations of sets associated to convex constraints. Finally, two applications are provided, which include elasto-plasticity and image restoration problems.
- ItemDuality results and regularization schemes for Prandtl-Reuss perfect plasticity(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Hintermüller, Michael; Rösel, SimonWe consider the time-discretized problem of the quasi-static evolution problem in perfect plasticity posed in a non-reflexive Banach space and we derive an equivalent version in a reflexive Banach space. A primal-dual stabilization scheme is shown to be consistent with the initial problem. As a consequence, not only stresses, but also displacement and strains are shown to converge to a solution of the original problem in a suitable topology. This scheme gives rise to a well-defined Fenchel dual problem which is a modification of the usual stress problem in perfect plasticity. The dual problem has a simpler structure and turns out to be well-suited for numerical purposes. For the corresponding subproblems an efficient algorithmic approach in the infinite-dimensional setting based on the semismooth Newton method is proposed.