An adaptive finite element method in quantitative reconstruction of small inclusions from limited observations

• 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Keyword

Adaptivity

Coefficient inverse problem

Finite element approximation

Adaptivity

Coefficient inverse problem

Finite element approximation

Publication and Content Type

art (subject category)

ref (subject category)