Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 331-347.
Published online: 2018-12
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We 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.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0124}, url = {http://global-sci.org/intro/article_detail/nmtma/12899.html} }We 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.