24 citations · 87 across the 19 of their papers we have counts for
21 papers
Combining diffuse and sharp interface methods in shape optimisation
Philip J. Herbert, Michael Hinze, Christian Kahle
We develop a concept for the numerical treatment of shape optimization problems based on the combination of phase field and sharp interface methods. On the one hand, phase field me…
A reduced basis method for parabolic PDEs based on a space-time least squares formulation
Michael Hinze, Christian Kahle, Michael Stahl
In this work, we present a POD-greedy reduced basis method for parabolic partial differential equations (PDEs), based on the least squares space-time formulation proposed in [Hinze…
Long-time behavior of solutions to a fluid dynamic shape optimization problem via phase-field method
Michael Hinze, Christian Kahle, John Sebastian H. Simon
We investigate the long time behavior of solutions to a shape and topology optimization problem with respect to the time-dependent Navier--Stokes equations. The sought topology is…
A least-squares space-time approach for parabolic equations
Michael Hinze, Christian Kahle, Michael Stahl
We propose a least squares formulation for abstract parabolic equations in the natural norm which only relies on natural regularity assumptions on the da…
Sharp-interface limit of a multi-phase spectral shape optimization problem for elastic structures
Harald Garcke, Paul Hüttl, Christian Kahle +1
We consider an optimization problem for the eigenvalues of a multi-material elastic structure that was previously introduced by Garcke et al. [Adv. Nonlinear Anal. 11 (2022), no. 1…
Phase-Field Methods for Spectral Shape and Topology Optimization
Harald Garcke, Paul Hüttl, Christian Kahle +2
We optimize a selection of eigenvalues of the Laplace operator with Dirichlet or Neumann boundary conditions by adjusting the shape of the domain on which the eigenvalue problem is…
Optimal Control of Droplets on a Solid Surface using Distributed Contact Angles
Henning Bonart, Christian Kahle, Jens-Uwe Repke
Controlling the shape and position of moving and pinned droplets on a solid surface is an important feature often found in microfluidic applications. However, automating them, e.g.…
Optimal Control of Sliding Droplets using the Contact Angle Distribution
Henning Bonart, Christian Kahle
Controlling the shape and position of moving and pinned droplets on a solid surface is an important feature often found in microfluidic applications. In this work, we consider a we…
Finite element error estimates in for regularized discrete approximations to the obstacle problem
Dominik Hafemeyer, Christian Kahle, Johannes Pfefferer
This work is concerned with quasi-optimal a-priori finite element error estimates for the obstacle problem in the -norm. The discrete approximations are introduced as solution…
A FEM for an optimal control problem subject to the fractional Laplace equation
Stefan Dohr, Christian Kahle, Sergejs Rogovs +1
We study the numerical approximation of linear-quadratic optimal control problems subject to the fractional Laplace equation with its spectral definition. We compute an approximati…
Comparison of Energy Stable Simulation of Moving Contact Line Problems using a Thermodynamically Consistent Cahn-Hilliard Navier-Stokes Model
Henning Bonart, Christian Kahle, Jens-Uwe Repke
Liquid droplets sliding along solid surfaces are a frequently observed phenomenon in nature, e.g., raindrops on a leaf, and in everyday situations, e.g., drops of water in a drinki…
Bayesian parameter identification in Cahn-Hilliard models for biological growth
Christian Kahle, Kei Fong Lam, Jonas Latz +1
We consider the inverse problem of parameter estimation in a diffuse interface model for tumour growth. The model consists of a fourth-order Cahn-Hilliard system and contains three…
Parameter identification via optimal control for a Cahn--Hilliard-chemotaxis system with a variable mobility
Christian Kahle, Kei Fong Lam
We consider the inverse problem of identifying parameters in a variant of the diffuse interface model for tumour growth model proposed by Garcke, Lam, Sitka and Styles (Math. Model…
A phase field approach to shape optimization in Navier--Stokes flow with integral state constraint
Harald Garcke, Michael Hinze, Christian Kahle +1
We consider the shape optimization of an object in Navier--Stokes flow by employing a combined phase field and porous medium approach, along with additional perimeter regularizatio…
Optimal Control of time-discrete two-phase flow driven by a diffuse-interface model
Harald Garcke, Michael Hinze, Christian Kahle
We propose a general control framework for two-phase flows with variable densities in the diffuse interface formulation, where the distribution of the fluid components is described…
Preconditioning of a coupled Cahn--Hilliard Navier--Stokes system
Jessica Bosch, Christian Kahle, Martin Stoll
Recently, Garcke et al.[Garcke, Hinze, Kahle, A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow, Applied Numerical…
Diffuse interface approaches in atmosphere and ocean - modeling and numerical implementation
Harald Garcke, Michael Hinze, Christian Kahle
We propose to model physical effects at the sharp density interface between atmosphere and ocean with the help of diffuse interface approaches for multiphase flows with variable de…
A bound for the Cahn--Hilliard equation with relaxed non-smooth free energy
Christian Kahle
Phase field models are widely used to describe multiphase systems. Here a smooth indicator function, called phase field, is used to describe the spatial distribution of the phases…
Shape optimization for surface functionals in Navier--Stokes flow using a phase field approach
Harald Garcke, Claudia Hecht, Michael Hinze +2
We consider shape and topology optimization for fluids which are governed by the Navier--Stokes equations. Shapes are modelled with the help of a phase field approach and the solid…
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…
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…