Simulation and Control of a Nonsmooth Cahn-Hilliard Navier–Stokes System with Variable Fluid Densities
Michael Hintermüller, Michael Hinze, Christian Kahle, Tobias Keil: A Goal-Oriented Dual-Weighted Adaptive Finite Element Approach for the Optimal Control of a Nonsmooth Cahn-Hilliard-Navier-Stokes System , Optimization and Engineering, 2018
Michael Hintermüller, Tobias Keil: Some Recent Developments in Optimal Control of Multiphase Flows, Shape Optimization, Homogenization and Optimal Control, 2018
Harald Garcke, Michael Hinze, Christian Kahle: Optimal Control of Time-Discrete Two-Phase Flow Driven by a Diffuse-Interface Model (SPP1962-058, 06/2018, [bib])
Harald Garcke, Michael Hinze, Christian Kahle, Kei Fong Lam: A Phase Field Approach to Shape Optimization in Navier--Stokes Flow with Integral State Constraints (SPP1962-059, 06/2018, [bib])
Harald Garcke, Claudia Hecht, Michael Hinze, Christian Kahle, Kei Fong Lam: Shape Optimization for Surface Functionals in Navier--Stokes Flow using a Phase Field Approach (SPP1962-060, 06/2018, [bib])
Carmen Gräßle, Michael Hinze: The Combination of POD Model Reduction with Adaptive Finite Element Methods in the Context of Phase Field Models (SPP1962-061, 06/2018, [bib])
Carmen Gräßle, Michael Hinze: POD Reduced Order Modeling for Evolution Equations Utilizing Arbitrary Finite Element Discretizations (SPP1962-010, 03/2017, [bib])
Michael Hintermüller, Michael Hinze, Christian Kahle, Tobias Keil: A Goal-Oriented Dual-Weighted Adaptive Finite Element Approach for the Optimal Control of a Nonsmooth Cahn-Hilliard-Navier-Stokes System (SPP1962-011, 03/2017, [bib])
Modeling, problem analysis, algorithm design and convergence analysisThe focus of this area is on the development and analysis of genuinely non-smooth models in the sciences in order to properly capture real-world effects and to avoid comprising smoothing approaches. In simulation and optimization this requires to advance set-valued analysis and the design of robust algorithms for non-smooth problems.
Realization of algorithms, adaptive discretization and model reductionAs the target applications of this SPP involve non-smooth structures and partial differential operators, the discretization of the associated problems and robust error estimation are important issues to be address, and proper model-reduction techniques need to be developed.
Project Related News
Oct 10, 2016 : Welcome to our new project member
Carmen Gräßle joins project 13.