Stable discretizations of elastic flow in riemannian manifolds

The elastic ow, which is the L2-gradient ow of the elastic energy, has several applications in geometry and elasticity theory. We present stable discretizations for the elastic ow in two-dimensional Riemannian manifolds that are conformally at, 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 Rd, d ≥ 3. Numerical results show the robustness of the method, as well as quadratic convergence with respect to the space discretization.