We consider the evolution of curves on surfaces. Basic equations to be solved are geodisc mean curvature flow and geodesic surface diffusion.
Two different numerical approaches are compared. 1) we use parametric finit elements to solve a level set equation for the evolution laws on a parametric surface, 2) we describe the surface implicitly as the zero level set of a function and use finite elements to solve a level set equation in the whole space, so basically solving a 3d problem to account for the movement of a 1d object.
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