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 ...
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.
Altmetric