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Stable discretizations of elastic flow in {R}iemannian manifolds

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Title: Stable discretizations of elastic flow in {R}iemannian manifolds
Authors: Barrett, JW
Garcke, H
Nürnberg, R
Item Type: Working Paper
Abstract: 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, the elliptic plane as well as any conformal parameterization of a two-dimensional manifold in ${\mathbb R}^d$, $d\geq 3$. Numerical results show the robustness of the method, as well as quadratic convergence with respect to the space discretization.
Issue Date: 1-Jan-2019
URI: http://hdl.handle.net/10044/1/70854
Keywords: math.NA
65M60, 53C44, 53A30, 35K55
Notes: 27 pages, 3 figures. This article is closely related to arXiv:1809.01973
Appears in Collections:Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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