188 citations · 1.6k across the 107 of their papers we have counts for
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On a Cahn-Hilliard-Brinkman model for tumour growth and its singular limits
Matthias Ebenbeck, Harald Garcke
In this work, we study a model consisting of a Cahn-Hilliard-type equation for the concentration of tumour cells coupled to a reaction-diffusion type equation for the nutrient dens…
Stable discretizations of elastic flow in Riemannian manifolds
John W. Barrett, Harald Garcke, Robert Nürnberg
The elastic flow, which is the -gradient flow of the elastic energy, has several applications in geometry and elasticity theory. We present stable discretizations for the elas…
Weak solutions of the Cahn-Hilliard system with dynamic boundary conditions: A gradient flow approach
Harald Garcke, Patrik Knopf
The Cahn-Hilliard equation is the most common model to describe phase separation processes of a mixture of two components. For a better description of short-range interactions of t…
Numerical approximation of curve evolutions in Riemannian manifolds
John W. Barrett, Harald Garcke, Robert Nürnberg
We introduce variational approximations for curve evolutions in two-dimensional Riemannian manifolds that are conformally flat, i.e.\ conformally equivalent to the Euclidean space.…
Analysis of a Cahn-Hilliard-Brinkman model for tumour growth with chemotaxis
Matthias Ebenbeck, Harald Garcke
Phase field models recently gained a lot of interest in the context of tumour growth models. Typically Darcy-type flow models are coupled to Cahn-Hilliard equations. However, often…
Finite element methods for fourth order axisymmetric geometric evolution equations
John W. Barrett, Harald Garcke, Robert Nürnberg
Fourth order curvature driven interface evolution equations frequently appear in the natural sciences. Often axisymmetric geometries are of interest, and in this situation numerica…