188 citations · 1.6k across the 107 of their papers we have counts for
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Sharp interface limit for a phase field model in structural optimization
Luise Blank, Harald Garcke, Claudia Hecht +1
We formulate a general shape and topology optimization problem in structural optimization by using a phase field approach. This problem is considered in view of well-posedness and…
Applying a phase field approach for shape optimization of a stationary Navier-Stokes flow
Harald Garcke, Claudia Hecht
We apply a phase field approach for a general shape optimization problem of a stationary Navier-Stokes flow. To be precise we add a multiple of the Ginzburg--Landau energy as a reg…
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…
Stability of Spherical Caps under the Volume-Preserving Mean Curvature Flow with Line Tension
Helmut Abels, Harald Garcke, Lars Müller
We show stability of spherical caps (SCs) lying on a flat surface, where the motion is governed by the volume-preserving Mean Curvature Flow (MCF). Moreover, we introduce a dynamic…
Stable Numerical Approximation of Two-Phase Flow with a Boussinesq--Scriven Surface Fluid
John W. Barrett, Harald Garcke, Robert Nürnberg
We consider two-phase Navier--Stokes flow with a Boussinesq--Scriven surface fluid. In such a fluid the rheological behaviour at the interface includes surface viscosity effects, i…
Local Well-Posedness for Volume-Preserving Mean Curvature and Willmore Flows with Line Tension
Helmut Abels, Harald Garcke, Lars Müller
We show the short-time existence and uniqueness of solutions for the motion of an evolving hypersurface in contact with a solid container driven by volume-preserving mean curvature…