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Stable Discretizations of Elastic Flow in Riemannian Manifolds

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


The elastic flow, which is the L-2-gradient flow of the elastic energy, has several applications in geometry and elasticity theory. We present stable discretizations for the elastic flow in two-dimensional Riemannian manifolds that are conformally flat, i.e., conformally equivalent to the Euclidean space. Examples include the hyperbolic plane, the hyperbolic disk, and the elliptic plane, as well ...


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