A stabilized nonconforming finite element method for the elliptic Cauchy problem

Source abstract

In this paper we propose a nonconforming finite element method for the solution of the ill-posed elliptic Cauchy problem. The recently derived framework from previous works of the author is extended to include the case of a nonconforming approximation space. We show that the use of such a space allows us to reduce the amount of stabilization necessary for convergence, even in the case of ill-posed problems. We derive error estimates using conditional stability estimates in the L 2 L^2 -norm.