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Particular features of implementation of an unsaturated numerical method for the exterior axisymmetric Neumann problem

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Abstract

Using Babenko’s profound ideas, we construct a fundamentally new unsaturated numerical method for solving the spectral problem for the operator of the exterior axisymmetric Neumann problem for Laplace’s equation. We estimate the deviation of the first eigenvalue of the discretized problem from the eigenvalue of the Neumann operator. More exactly, the unsaturated discretization of the spectral Neumann problem yields an algebraic problem with a good matrix, i.e., a matrix inheriting the spectral properties of the Neumann operator. Thus, its spectral portrait lacks “parasitic” eigenvalues provided that the discretization error is sufficiently small. The error estimate for the first eigenvalue involves efficiently computable parameters, which in the case of C ∞-smooth data provides a foundation for a guaranteed success.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    V. N. Belykh

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  1. V. N. Belykh
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Correspondence to V. N. Belykh.

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Original Russian Text Copyright © 2013 Belykh V.N.

The author was supported by the Russian Foundation for Basic Research (Grants 11-01-00147-a and 12-01-00061-a).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 6, pp. 1237–1249, November–December, 2013.

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Belykh, V.N. Particular features of implementation of an unsaturated numerical method for the exterior axisymmetric Neumann problem. Sib Math J 54, 984–993 (2013). https://doi.org/10.1134/S0037446613060037

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