Analysis of Lavrentiev-finite element methods for data completion problems

The variational finite element solution of Cauchy’s problem, expressed in the Steklov–Poincaré framework and regularized by the Lavrentiev method, has been introduced and computationally assessed in Azaïez et al. (Inverse Probl Sci Eng 18:1063–1086, 2011 ). The present work concentrates on the numerical analysis of the semi-discrete problem. We perform the mathematical study of the error to rigorously establish the convergence of the global bias-variance error.