  We consider solving the Laplace-Beltrami problem on a smooth two dimensional
surface embedded into a three dimensional space meshed with tetrahedra. The
mesh does not respect the surface and thus the surface cuts through the
elements. We consider a Galerkin method based on using the restrictions of
continuous piecewise linears defined on the tetrahedra to the surface as trial
and test functions.
  The resulting discrete method may be severely ill-conditioned, and the main
purpose of this paper is to suggest a remedy for this problem based on adding a
consistent stabilization term to the original bilinear form. We show optimal
estimates for the condition number of the stabilized method independent of the
location of the surface. We also prove optimal a priori error estimates for the
stabilized method.
