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- W2034342256 abstract "We study an example of the class of inverse source problems: to determine the source field of the Poisson equation from a finite number of density field measurements. Such problems are not well-posed, hence we consider reconstructions obtained using Tikhonov regularization. The regularized problem can in general only be solved using a numerical method, which introduces an approximation error. We consider approximations obtained using the finite element method and derive a priori error estimates for the numerical error. Our estimates allow different regularization terms, e.g. L2 and H1 regularization, and are expressed with respect to the finite element mesh sizes used to discretize the forward and the inverse problems. The novelty of our approach is that we consider finite measurement data, whereas the existing work assumes infinite dimensional measurements. The obtained results are illustrated by three numerical experiments. These examples cover situations where the solution regularity is high, as well as situations where the regularity is low. In addition, measurements in the interior of the domain and measurements on the boundary of the domain are both investigated. The numerical tests verify that the derived a priori error estimates work well in these different situations." @default.
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- W2034342256 date "2014-07-25" @default.
- W2034342256 modified "2023-09-26" @default.
- W2034342256 title "A priori error estimate of the finite element solution to a Poisson inverse source problem" @default.
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- W2034342256 doi "https://doi.org/10.1088/0266-5611/30/8/085007" @default.
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