Geodesic
An adaptive finite element method in reconstruction of coefficients in Maxwell's equations from limited observations
Applications of Mathematics, Tome 61 (2016) no. 3, pp. 253-286.

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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.
DOI : 10.1007/s10492-016-0131-0
Classification : 65M06, 65M22, 65M32, 65M60, 65N30
Keywords: Maxwell's system; coefficient inverse problem; Tikhonov functional; Lagrangian approach; a posteriori error estimate 
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     title = {An adaptive finite element method in reconstruction of coefficients in {Maxwell's} equations from limited observations},
     journal = {Applications of Mathematics},
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Beilina, Larisa; Hosseinzadegan, Samar. An adaptive finite element method in reconstruction of coefficients in Maxwell's equations from limited observations. Applications of Mathematics, Tome 61 (2016) no. 3, pp. 253-286. doi : 10.1007/s10492-016-0131-0. http://geodesic.mathdoc.fr/articles/10.1007/s10492-016-0131-0/

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