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TAYLOR & FRANCIS LTD
DOI: 10.1080/02331934.2022.2141572
Keywords
Inverse source problem; elliptic equations; ill-posedness; regularization; finite element method
Funding
- Vietnam Institute for Advanced Study inMathematics (VIASM)
- International Center for Research and Postgraduate Training inMathematics, Institute of Mathematics, VAST [ICRTM02-2020.03]
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This research investigates the problem of determining a term in the right-hand side of elliptic equations from an observation on a part of the boundary. The inverse problem is formulated as an operator equation and stabilized using the Tikhonov regularization method. The regularized problem is discretized based on Hinze's variational discretization concept, and the performance is demonstrated through numerical examples.
The problem of determining a term in the right-hand side of elliptic equations from an observation on a part of the boundary is investigated. The inverse problem is formulated as an operator equation and then stabilized by Tikhonov regularization method. The regularized problem is discretized based on Hinze's variational discretization concept and the regularization parameter is chosen guaranteeing that when noise level and the discretization mesh size tend to zero, the solution of the discretized regularized problem converges to the f*-minimum norm solution of the continuous inverse problem. Some numerical examples are presented for illustrating the performance of the proposed method.
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