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Applications of Mathematics

, Volume 61, Issue 3, pp 253–286 | Cite as

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

  • Larisa Beilina
  • Samar Hosseinzadegan
Article

Abstract

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.

Keywords

Maxwell’s system coefficient inverse problem Tikhonov functional Lagrangian approach a posteriori error estimate 

MSC 2010

65M06 65N30 65M60 65M22 65M32 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2016

Authors and Affiliations

  1. 1.Department of Mathematical SciencesChalmers University of Technology and Gothenburg UniversityGöteborgSweden
  2. 2.Department of Signals and SystemsChalmers University of TechnologyGöteborgSweden

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