Surface meshing using a geometric error estimate

In this paper we discuss an a posteriori interpolation error estimate based on the Hessian of the surface and we propose a new geometric error estimate related to the local deformation of the surface. The new approach makes possible the construction of adapted geometric meshes for surfaces by specifying the element sizes (and directions) so as to bound the error below a user-given threshold value. The surfaces considered here are Cartesian surfaces. An analytical example is provided so as to emphasize the potential of the approach