Abstract
The paper is concerned with analysis of elliptic boundary value problems, where the operator is not completely known. Instead, some mean operator and admissible magnitude of perturbations is known. It is assumed that the perturbed operator remains symmetric. These “equally possible” perturbed operators generate a set of respective solutions. In this paper, two-sided bound for the radius of the solution set are deduced using the duality theory. The bounds are explicitly computable. They show the accuracy limit dictated by the incompletely known data and can be used in cooperation with various numerical methods in order to obtain a reasonable stopping criteria for adaptive methods.
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Communicated by Ragnar Winther.
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Mali, O., Repin, S. Estimates of the solution set for a class of elliptic problems with incompletely known data. Bit Numer Math 56, 163–188 (2016). https://doi.org/10.1007/s10543-015-0552-2
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DOI: https://doi.org/10.1007/s10543-015-0552-2