A numerical approach for the determination of a missing boundary data in elliptic problems

摘要

We consider the problem of the recovery of an unknown transfer coefficient in the Robin boundary condition on an inaccessible part of the boundary of an elliptic boundary value problem. The physical process inside the domain is governed by a linear elliptic equation of second order. The unknown boundary data are determined from superfluous information on the accessible part of the boundary. We show that the inverse problem is equivalent to a system of direct problems. We design a numerical approach for thin domains. The method is tested by numerical experiments.