Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem
Artikel i vetenskaplig tidskrift, 2010

A new framework of the functional analysis is developed for the finite element adaptive method (adaptivity) for the Tikhonov regularization functional for some ill-posed problems. As a result, the relaxation property for adaptive mesh refinements is established. An application to a multidimensional coefficient inverse problem for a hyperbolic equation is discussed. This problem arises in the inverse scattering of acoustic and electromagnetic waves. First, a globally convergent numerical method provides a good approximation for the correct solution of this problem. Next, this approximation is enhanced via the subsequent application of the adaptivity. Analytical results are verified computationally. Bibliography: 30 titles. Illustration: 2 figures.


Larisa Beilina

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Michael V. Klibanov

The University of North Carolina at Charlotte

Mikhail Yu. Kokurin

Mari State University

Journal of Mathematical Sciences

1072-3374 (ISSN)

Vol. 167 279-325