Superconvergent Algorithms for the Numerical Solution of the Laplace Equation in Smooth Axisymmetric Domains Full article
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Computational Mathematics and Mathematical Physics
ISSN: 0965-5425 , E-ISSN: 1555-6662 |
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| Output data | Year: 2020, Volume: 60, Number: 4, Pages: 545-557 Pages count : 13 DOI: 10.1134/S096554252004003X | ||
| Tags | axial symmetry; exponential convergence; Laplace equation; nonsaturable numerical method; well-posedness | ||
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Abstract:
Abstract: A fundamentally new—nonsaturable—method is constructed for the numerical solution of elliptic boundary value problems for the Laplace equation in C∞-smooth axisymmetric domains of fairly arbitrary shape. A distinctive feature of the method is that it has a zero leading error term. As a result, the method is automatically adjusted to any redundant (extraordinary) smoothness of the solutions to be found. The method enriches practice with a new computational tool capable of inheriting, in discretized form, both differential and spectral characteristics of the operator of the problem under study. This underlies the construction of a numerical solution of guaranteed quality (accuracy) if the elliptic problem under study has a sufficiently smooth (e.g., C∞-smooth) solution. The result obtained is of fundamental importance, since, in the case of C∞-smooth solutions, the solution is constructed with an absolutely sharp exponential error estimate. The sharpness of the estimate is caused by the fact that the Aleksandrov m-width of the compact set of C∞-smooth functions, which contains the exact solution of the problem, is asymptotically represented in the form of an exponential function decaying to zero (with growing integer parameter m). © 2020, Pleiades Publishing, Ltd.
Cite:
Belykh V.N.
Superconvergent Algorithms for the Numerical Solution of the Laplace Equation in Smooth Axisymmetric Domains
Computational Mathematics and Mathematical Physics. 2020. V.60. N4. P.545-557. DOI: 10.1134/S096554252004003X WOS Scopus OpenAlex
Superconvergent Algorithms for the Numerical Solution of the Laplace Equation in Smooth Axisymmetric Domains
Computational Mathematics and Mathematical Physics. 2020. V.60. N4. P.545-557. DOI: 10.1134/S096554252004003X WOS Scopus OpenAlex
Original:
Белых В.Н.
Сверхсходящиеся алгоритмы численного решения уравнения Лапласа в гладких осесимметричных областях
Журнал вычислительной математики и математической физики. 2020. Т.60. №4. С.553-566. DOI: 10.31857/S0044466920040031 OpenAlex
Сверхсходящиеся алгоритмы численного решения уравнения Лапласа в гладких осесимметричных областях
Журнал вычислительной математики и математической физики. 2020. Т.60. №4. С.553-566. DOI: 10.31857/S0044466920040031 OpenAlex
Identifiers:
| Web of science: | WOS:000539033500001 |
| Scopus: | 2-s2.0-85086228130 |
| OpenAlex: | W3035689555 |