Larisa Beulina
Chalmers University of Technology
Göteborg
An adaptive finite element method for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and the magnetic permeability functions in the Maxwell's system will be presented. This method uses only limited boundary observations of the electric field.
We will show the main steps of the derivation of a posteriori error estimates in the Tikhonov functional to be minimized and in the regularized solution of this functional. The corresponding adaptive algorithm will be presented.
Numerical experiments will justify the efficiency of the a posteriori estimates and will show significant improvement of the reconstructions obtained on a locally adaptively refined meshes.
Additional literature:
http://www.math.chalmers.se/~larisa/www/PAPERS/Papers.zip