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An adaptive finite ...
An adaptive finite element method in reconstruction of coefficients in Maxwell's equations from limited observations
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- Beilina, Larisa, 1970 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg
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- Hosseinzadegan, Samar, 1987 (author)
- Chalmers tekniska högskola,Chalmers University of Technology
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(creator_code:org_t)
- 2016-05-18
- 2016
- English.
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In: Applications of Mathematics. - : Institute of Mathematics, Czech Academy of Sciences. - 0862-7940 .- 1572-9109. ; 61:3, s. 253-286
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Abstract
Subject headings
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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.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- Maxwell's system
- coefficient inverse problem
- Tikhonov functional
- Lagrangian approach
- a posteriori error estimate
- Lagrangian approach
Publication and Content Type
- ref (subject category)
- art (subject category)
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