An adaptive finite element method in reconstruction of coefficients in Maxwell's equations from limited observations

摘要

We propose an adaptive finite element method for the solution of acoefficient inverse problem of simultaneous reconstruction of the dielectricpermittivity and magnetic permeability functions in the Maxwell's system usinglimited boundary observations of the electric field in 3D. We derive aposteriori error estimates in the Tikhonov functional to be minimized and inthe regularized solution of this functional, as well as formulate correspondingadaptive algorithm. Our numerical experiments justify the efficiency of our aposteriori estimates and show significant improvement of the reconstructionsobtained on locally adaptively refined meshes.