Numerical estimation of the Robin coefficient in a stationary diffusion equation
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AbstractA finite-element method is proposed for the nonlinear inverse problem of estimating the Robin coefficient in a stationary diffusion equation from boundary measurements of the solution and the heat flux. The inverse problem is formulated as an output least squares optimization problem with an appropriate regularization, then the finite-element method is employed to discretize the nonlinear optimization system. Mathematical properties of both the continuous and the discrete optimization problems are investigated. The conjugate gradient method is employed to solve the optimization problem, and an efficient preconditioner via the Sobolev inner product is also suggested. Numerical results for several two-dimensional problems are presented to illustrate the efficiency of the proposed algorithm. © 2009 The author. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
All Author(s) ListJin B., Zou J.
Journal nameIMA Journal of Numerical Analysis
Year2010
Month7
Day1
Volume Number30
Issue Number3
PublisherOxford University Press
Place of PublicationUnited Kingdom
Pages677 - 701
ISSN0272-4979
eISSN1464-3642
LanguagesEnglish-United Kingdom
Keywordsconjugate gradient method, finite-element method, Robin inverse problem, Sobolev gradient, stationary diffusion equation

Last updated on 2020-06-08 at 00:38