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Stable variational approximations of boundary value problems for Willmore flow with Gaussian curvature

Nürnberg, Robert ; Garcke, Harald ; Barrett, John W.


We study numerical approximations for geometric evolution equations arising as gradient flows for energy functionals that are quadratic in the principal curvatures of a two-dimensional surface. Besides the well-known Willmore and Helfrich flows, we will also consider flows involving the Gaussian curvature of the surface. Boundary conditions for these flows are highly nonlinear, and we use a ...


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