404 citations · 3.5k across the 79 of their papers we have counts for
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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…
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.…
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…
Variational discretization of axisymmetric curvature flows
John W. Barrett, Harald Garcke, Robert Nürnberg
We present natural axisymmetric variants of schemes for curvature flows introduced earlier by the present authors and analyze them in detail. Although numerical methods for geometr…