Goal oriented adaptivity in the IRGNM for parameter identification in PDEs: I. reduced formulation

DOI10.1088/0266-5611/30/4/045001zbMath1303.65044arXiv1309.6800OpenAlexW3105686119MaRDI QIDQ5418604

Alana Kirchner, Slobodan Veljović, Barbara Kaltenbacher

Publication date: 26 May 2014

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.6800

zbMATH Keywords

inverse problemHilbert spaceparameter identificationBanach spaceconvergence ratediscrepancy principleill-posed problemsource conditionBregman distancea posteriori parameter choiceadaptive discretizationa priori parameter choiceiteratively regularized Gauss-Newton method

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Numerical solution to inverse problems in abstract spaces (65J22) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

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Convergence and adaptive discretization of the IRGNM Tikhonov and the IRGNM Ivanov method under a tangential cone condition in Banach space ⋮ The Ivanov regularized Gauss-Newton method in Banach space with an a posteriori choice of the regularization radius

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