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Adaptivity with rel...
Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem
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- Beilina, Larisa, 1970 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, matematik,Department of Mathematical Sciences, Mathematics,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg
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- Klibanov, Michael V. (author)
- The University of North Carolina at Charlotte
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- Kokurin, Mikhail Yu. (author)
- Mari State University
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(creator_code:org_t)
- 2010-05-20
- 2010
- English.
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In: Journal of Mathematical Sciences, JMS, Springer. - : Springer Science and Business Media LLC. - 1072-3374 .- 1573-8795. ; 167:3, s. 279-325
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Abstract
Subject headings
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Publication and Content Type
- ref (subject category)
- art (subject category)
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