Section: New Results

Data completion problems for elliptic equations using the theory of factorization

Participants : Jacques Henry, Fadhel Jday.

This is the topic of F. Jday's thesis co-supervised by A. Ben Abda and J. Henry within the “équipe associée” Enée 06. The data completion problem for elliptic equations consists in finding the best approximation of lacking boundary data on certain part of the boundary using extra measurements on other parts of the boundary. F. Jday investigates the data completion problem in a cylindrical domain where the factorisation method is most easily applied. It is formulated as a control in the Kohn-Vogelius setting with two states. There is no need to introduce adjoint variables in this case as the cost function can be expressed directly in terms of the control variables with the use of the operators furnished by the factorisation. New boundary conditions as the Fourier conditions have been studied. Numerical results show the benefits of the method when the same problem has to be solved with various data.