  We consider finite element approximations of unique continuation problems
subject to elliptic equations in the case where the normal derivative of the
exact solution is known to reside in some finite dimensional space. To give
quantitative error estimates we prove Lipschitz stability of the unique
continuation problem in the global H1-norm. This stability is then leveraged to
derive optimal a posteriori and a priori error estimates for a primal-dual
stabilised finite method.
