An adaptive finite element method in quantitative reconstruction of small inclusions from limited observations
Journal article, 2018

We consider a coefficient inverse problem to determine the dielectric permittivity in Maxwell's equations, with data consisting of boundary measurements. The true dielectric permittivity is assumed to belong to an ideal space of very fine finite elements. The problem is treated using a Lagrangian approach to the minimization of a Tikhonov functional, where an adaptive finite element method forms the basis of the computations. A new a posteriori error estimate for the norm of the error in the reconstructed permittivity is derived. The adaptive algorithm is formulated and tested successfully in numerical experiments for the reconstruction of two, three, and four small inclusions with low contrast, as well as the reconstruction of a superposition of two Gaussian functions.

Finite element approximation

Adaptivity

Coefficient inverse problem

Author

John Bondestam Malmberg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Larisa Beilina

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Applied Mathematics and Information Sciences

1935-0090 (ISSN)

Vol. 12 1 1-19

Subject Categories

Computational Mathematics

Control Engineering

Mathematical Analysis

DOI

10.18576/amis/120101

More information

Latest update

4/20/2018