20 citations · 52 across the 33 of their papers we have counts for
5 papers · 1 filter
Numerical approximation of optimal convex shapes
Sören Bartels, Gerd Wachsmuth
This article investigates the numerical approximation of shape optimization problems with PDE constraint on classes of convex domains. The convexity constraint provides a compactne…
Optimal control of ODEs with state suprema
Tobias Geiger, Daniel Wachsmuth, Gerd Wachsmuth
We consider the optimal control of a differential equation that involves the suprema of the state over some part of the history. In many applications, this non-smooth functional de…
First and Second Order Shape Optimization based on Restricted Mesh Deformations
Tommy Etling, Roland Herzog, Estefanía Loayza +1
We consider shape optimization problems subject to elliptic partial differential equations. In the context of the finite element method, the geometry to be optimized is represented…
Generalized derivatives for the solution operator of the obstacle problem
Anne-Therese Rauls, Gerd Wachsmuth
We characterize generalized derivatives of the solution operator of the obstacle problem. This precise characterization requires the usage of the theory of so-called capacitary mea…
Discrete Total Variation with Finite Elements and Applications to Imaging
Marc Herrmann, Roland Herzog, Stephan Schmidt +2
The total variation (TV)-seminorm is considered for piecewise polynomial, globally discontinuous (DG) and continuous (CG) finite element functions on simplicial meshes. A novel, di…