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.

翻译：我们考虑精确解的法向导数已知位于某个有限维空间中的椭圆型方程唯一延拓问题的有限元逼近。为给出定量误差估计，我们证明了全局H1范数下唯一延拓问题的Lipschitz稳定性。进而利用该稳定性，为原始-对偶稳定化有限元方法推导出最优后验和先验误差估计。