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arXiv · 1502.07658

A posteriori error estimation in a finite element method for reconstruction of dielectric permittivity

John Bondestam Malmberg
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Abstract

We present a posteriori error estimates for finite element approximations in a minimization approach to a coefficient inverse problem. The problem is that of reconstructing the dielectric permittivity $\varepsilon = \varepsilon(\mathbf{x})$, $\mathbf{x}\in\Omega\subset\mathbb{R}^3$, from boundary measurements of the electric field. The electric field is related to the permittivity via Maxwell's equations. The reconstruction procedure is based on minimization of a Tikhonov functional where the permittivity, the electric field and a Lagrangian multiplier function are approximated by peicewise polynomials. Our main result is an estimate for the difference between the computed coefficient $\varepsilon_h$ and the true minimizer $\varepsilon$, in terms of the computed functions.

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John Bondestam Malmberg. 2015-02-26. A posteriori error estimation in a finite element method for reconstruction of dielectric permittivity. https://arxiv.org/abs/1502.07658

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