An adaptive finite element method in reconstruction of coefficients in Maxwell's equations from limited observations
Journal article, 2016

We propose an adaptive finite element method for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions in the Maxwell's system using limited boundary observations of the electric field in 3D. We derive a posteriori error estimates in the Tikhonov functional to be minimized and in the regularized solution of this functional, as well as formulate the corresponding adaptive algorithm. Our numerical experiments justify the efficiency of our a posteriori estimates and show significant improvement of the reconstructions obtained on locally adaptively refined meshes.

Tikhonov functional

coefficient inverse problem

Maxwell's system

a posteriori error estimate

Lagrangian approach


Larisa Beilina

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Samar Hosseinzadegan

Chalmers, Signals and Systems, Signalbehandling och medicinsk teknik, Biomedical Electromagnetics

Applications of Mathematics

0862-7940 (ISSN)

Vol. 61 3 253-286

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