A New Variational Approach for Inverse Source Problems
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AbstractWe propose a new variational approach for recovering a general source profile in an elliptic system, using measurement data from the interior of the physical domain. The solution of the ill-posed inverse source problem is achieved by solving only one well-posed direct elliptic problem, resulting in the same computational cost as the one for the direct problem, and hence making the whole solution process of the inverse problem much less expensive than most existing methods. The resulting approximate solution is shown to be stable with respect to the change of the noise in the observation data, and a desired error estimate is also established in terms of the mesh size and the noise level in observation data. Numerical experiments are presented to confirm the theoretical predictions.
Acceptance Date18/03/2018
All Author(s) ListQiya Hu, Shi Shu, Jun Zou
Journal nameNumerical Mathematics
Year2019
Month5
Volume Number12
Issue Number2
PublisherGlobal-Science Press
Pages331 - 347
ISSN1004-8979
eISSN2079-7338
LanguagesEnglish-United States
KeywordsVariational approach, inverse source problem, stability, convergence

Last updated on 2020-28-03 at 02:50