Summary.
This paper is concerned with the ill-posed problem of identifying a parameter in an elliptic equation and its solution applying regularization by projection. As the theory has shown, the ansatz functions for the parameter have to be sufficiently smooth. In this paper we show that these – for a practical implementation unrealistic – smoothness assumptions can be circumvented by reformulating the problem under consideration as a mixed variational equation. We prove convergence as the discretization gets finer in the noise free case and convergence as the data noise level \(\delta\) goes to zero in the case of noisy data, as well as convergence rates under additional smoothness conditions.
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Received August 4, 2000 / Revised version received March 21, 2001 / Published online October 17, 2001
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Kaltenbacher, B., Schöberl, J. A saddle point variational formulation for projection–regularized parameter identification. Numer. Math. 91, 675–697 (2002). https://doi.org/10.1007/s002110100350
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DOI: https://doi.org/10.1007/s002110100350