  A new concept for the higher-order accurate approximation of partial
differential equations on manifolds is proposed where a surface mesh composed
by higher-order elements is automatically generated based on level-set data.
Thereby, it enables a completely automatic workflow from the geometric
description to the numerical analysis without any user-intervention. A master
level-set function defines the shape of the manifold through its
zero-isosurface which is then restricted to a finite domain by additional
level-set functions. It is ensured that the surface elements are sufficiently
continuous and shape regular which is achieved by manipulating the background
mesh. The numerical results show that optimal convergence rates are obtained
with a moderate increase in the condition number compared to handcrafted
surface meshes.
