Abstract
An inverse source problem of the Poisson equation is discussed with a boundary-element-like method. This method is based on a boundary integral expression of the Poisson equation. With this method, we can eliminate the harmonic term in the solution of the Poisson equation using the solution and flux on the boundary and consider only an inverse problem of the logarithmic potential. A simple model is used for the source term, and an effective numerical algorithm is presented for the determination of the source in this model. A precise error bound for the result is also given in the case of constant elements on the boundary. The applicability of our method and error estimates is illustrated by a numerical example.
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