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

Författare och institution:
Larisa Beilina (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU); Michael V. Klibanov (-); Mikhail Yu. Kokurin (-)
Publicerad i:
Journal of Mathematical Sciences, JMS, Springer, 167 ( 3 ) s. 279-325
ISSN:
1072-3374
Publikationstyp:
Artikel, refereegranskad vetenskaplig
Publiceringsår:
2010
Språk:
engelska
Fulltextlänk:
Sammanfattning (abstract):
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.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik ->
Beräkningsmatematik ->
Tillämpad matematik
Postens nummer:
131090
Posten skapad:
2010-12-16 14:46
Posten ändrad:
2016-07-14 11:12

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