Stable Discretizations of Elastic Flow in Riemannian Manifolds
| Autor: | John W. Barrett, Robert Nürnberg, Harald Garcke |
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| Rok vydání: | 2019 |
| Předmět: |
Mathematics - Differential Geometry
Hyperbolic geometry Stability (probability) Equidistribution Physics::Fluid Dynamics Riemannian manifolds 65M60 53C44 53A30 35K55 Hyperbolic plane FOS: Mathematics Mathematics - Numerical Analysis Mathematics Numerical Analysis Applied Mathematics Mathematical analysis Elastic energy Elasticflow Elliptic plane Finite element approximation Geodesic elasticflow Hyperbolic disk Stability Numerical Analysis (math.NA) Computational Mathematics Differential Geometry (math.DG) Flow (mathematics) |
| Zdroj: | SIAM Journal on Numerical Analysis. 57:1987-2018 |
| ISSN: | 1095-7170 0036-1429 |
| DOI: | 10.1137/18m1227111 |
| Popis: | 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. Minor revision. 31 pages, 6 figures. This article is closely related to arXiv:1809.01973 |
| Databáze: | OpenAIRE |
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