Barrett, John W. and Garcke, Harald and Nurnberg, Robert (2019) STABLE DISCRETIZATIONS OF ELASTIC FLOW IN RIEMANNIAN MANIFOLDS. SIAM JOURNAL ON NUMERICAL ANALYSIS, 57 (4). pp. 1987-2018. ISSN 0036-1429, 1095-7170
Full text not available from this repository. (Request a copy)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, and the elliptic plane, as well as any conformal parameterization of a two-dimensional manifold in R-d, d >= 3. Numerical results show the robustness of the method, as well as quadratic convergence with respect to the space discretization.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PERIODIC GEODESICS; APPROXIMATION; CURVATURE; EVOLUTION; CURVES; elastic flow; hyperbolic plane; hyperbolic disk; elliptic plane; Riemannian manifolds; geodesic elastic flow; finite element approximation; stability; equidistribution |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 27 Apr 2020 09:40 |
| Last Modified: | 27 Apr 2020 09:40 |
| URI: | https://pred.uni-regensburg.de/id/eprint/27778 |
Actions (login required)
 |
View Item |
