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Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem

Larisa Beilina (Institutionen för matematiska vetenskaper, matematik) ; Michael V. Klibanov ; Mikhail Yu. Kokurin
Journal of Mathematical Sciences, JMS, Springer (1072-3374). Vol. 167 (2010), 3, p. 279-325.
[Artikel, refereegranskad vetenskaplig]

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.



Denna post skapades 2010-12-16. Senast ändrad 2016-07-14.
CPL Pubid: 131090

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Tillämpad matematik

Chalmers infrastruktur