26 citations · 164 across the 38 of their papers we have counts for
5 papers · 1 filter
A finite element method for Dirichlet boundary control problems governed by parabolic PDEs
Wei Gong, Michael Hinze, Zhaojie Zhou
Finite element approximations of Dirichlet boundary control problems governed by parabolic PDEs on convex polygonal domains are studied in this paper. The existence of a unique sol…
Numerical approximation of phase field based shape and topology optimization for fluids
Harald Garcke, Claudia Hecht, Michael Hinze +1
We consider the problem of finding optimal shapes of fluid domains. The fluid obeys the Navier--Stokes equations. Inside a holdall container we use a phase field approach using dif…
HJB-POD feedback control for Navier-Stokes equations
Alessandro Alla, Michael Hinze
In this report we present the approximation of an infinite horizon optimal control problem for the evolutive Navier-Stokes system. The method is based on a model reduction techniqu…
Crank-Nicolson time stepping and variational discretization of control-constrained parabolic optimal control problems
Nikolaus von Daniels, Michael Hinze, Morten Vierling
We consider a control constrained parabolic optimal control problem and use variational discretization for its time semi-discretization. The state equation is treated with a Petrov…
A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow
Harald Garcke, Michael Hinze, Christian Kahle
A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consi…