Results for "Winnifried Wollner"

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A Stochastic Gradient Method with Mesh Refinement for PDE Constrained Optimization under UncertaintyMay 21 2019Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE constrained optimization. In this paper, we focus on the efficient numerical solution to minimizing a convex and smooth tracking-type ... More
A phase-field model for fractures in incompressible solidsJan 16 2019Within this work, we develop a phase-field description for simulating fractures in incompressible materials. Standard formulations are subject to volume-locking when the solid is (nearly) incompressible. We propose an approach that builds on a mixed form ... More
Mesh adaptivity for quasi-static phase-field fractures based on a residual-type a posteriori error estimatorJun 11 2019In this work, we consider adaptive mesh refinement for a monolithic phase-field description for fractures in brittle materials. Our approach is based on an a posteriori error estimator for the phase-field variational inequality realizing the fracture ... More
Quasi-best approximation in optimization with PDE constraintsApr 15 2019We consider finite element solutions to quadratic optimization problems, where the state depends on the control via a well-posed linear partial differential equation. Exploiting the structure of a suitably reduced optimality system, we prove that the ... More
Multigoal-oriented optimal control problems with nonlinear PDE constraintsMar 07 2019In this work, we consider an optimal control problem subject to a nonlinear PDE constraint and apply it to the regularized $p$-Laplace equation. To this end, a reduced unconstrained optimization problem in terms of the control variable is formulated. ... More