  We consider a diffuse interface approach for solving an elliptic PDE on a
given closed hypersurface. The method is based on a (bulk) finite element
scheme employing numerical quadrature for the phase field function and hence is
very easy to implement compared to other approaches. We estimate the error in
natural norms in terms of the spatial grid size, the interface width and the
order of the underlying quadrature rule. Numerical test calculations are
presented which confirm the form of the error bounds.
