Analysis of Lavrentiev-finite element methods for data completion problems (Q1749435)

A variational formulation for the Cauchy problem, proposed by the first author in earlier collaborative works, has been shown to be a suitable framework where Lavrentiev's regularization has been applied. It is also a useful tool in analyzing the problem and demonstrating important properties related to its ill-posedness. Since a convergence analysis of the full approximation is really hard, the authors of the present work explore the first step by presenting a numerical analysis of the semi-discrete problem, where the use of finite elements is restricted to the incomplete boundary. Among other things, the convergence of the global bias-variance error is established.