FULL DISCRETIZATION OF CAUCHY'S PROBLEM BY LAVRENTIEV-FINITE ELEMENT METHOD

We conduct a detailed study of the fully discrete finite element approximation of the data completion problem. This is the continuation of [Numer. Math., 139 (2016), pp. 1-25], where the variational problem, resulting from the Kohn-Vogelius duplication framed into the Steklov-Poincare condensation approach, was semidiscretized. Under the condition that the problem has a solution, we derive a bound of the error with respect to the mesh-size and the Lavrentiev regularization parameter. Sharp local finite element estimates, such as those derived by Nitsche and Schatz [Math. Comp., 28 (1974), pp. 937-958], are the central technical tools of the analysis.

Automated summary

This study focuses on the fully discrete finite element approximation of the data completion problem and derives an error bound with respect to mesh-size and regularization parameter. The central technical tools used in the analysis are sharp local finite element estimates derived by Nitsche and Schatz.