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Relaxation property for the adaptivity for ill-posed problems

Larisa Beilina (Institutionen för matematiska vetenskaper, matematik) ; M.V. Klibanov
Applicable Analysis (0003-6811). Vol. 93 (2014), 2, p. 223-253.
[Artikel, refereegranskad vetenskaplig]

Adaptive finite element method (adaptivity) is known to be an effective numerical tool for some ill-posed problems. The key advantage of the adaptivity is the image improvement with local mesh refinements. A rigorous proof of this property is the central part of this paper. In terms of coefficient inverse problems with single measurement data, the authors consider the adaptivity as the second stage of a two-stage numerical procedure. The first stage delivers a good approximation of the exact coefficient without an advanced knowledge of a small neighborhood of that coefficient. This is a necessary element for the adaptivity to start iterations from. Numerical results for the two-stage procedure are presented for both computationally simulated and experimental data.

Nyckelord: adaptive finite element method , coefficient inverse problem , ill-posed problems , numerical studies , relaxation property

Denna post skapades 2013-12-28. Senast ändrad 2014-04-10.
CPL Pubid: 190562


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