Two Tikhonov‐type regularization methods for inverse source problem on the Poisson equation |
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Authors: | Jingjun Zhao Songshu Liu Tao Liu |
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Institution: | Department of Mathematics, Harbin Institute of Technology, , Harbin, 150001 China |
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Abstract: | In this paper, we investigate a problem of the identification of an unknown source on Poisson equation from some fixed location. A conditional stability estimate for an inverse heat source problem is proved. We show that such a problem is mildly ill‐posed and further present two Tikhonov‐type regularization methods (a generalized Tikhonov regularization method and a simplified generalized Tikhonov regularization method) to deal with this problem. Convergence estimates are presented under the a priori choice of the regularization parameter. Numerical results are presented to illustrate the accuracy and efficiency of our methods. Copyright © 2012 John Wiley & Sons, Ltd. |
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Keywords: | ill‐posed problems inverse problems stability estimate generalized Tikhonov regularization method unknown source Poisson equation |
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