A stabilized nonconforming finite element method for the elliptic Cauchy problem

Burman, Erik

doi:10.1090/mcom/3092

A stabilized nonconforming finite element method for the elliptic Cauchy problem
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Math. Comp. 86 (2017), 75-96 Request permission

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 $L^2$-norm.

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