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- Title
Superconvergent Algorithms for the Numerical Solution of the Laplace Equation in Smooth Axisymmetric Domains.
- Authors
Belykh, V. N.
- Abstract
A fundamentally new—nonsaturable—method is constructed for the numerical solution of elliptic boundary value problems for the Laplace equation in -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., -smooth) solution. The result obtained is of fundamental importance, since, in the case of -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 -width of the compact set of -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
- Subjects
NUMERICAL solutions to equations; NUMERICAL solutions to boundary value problems; LAPLACE transformation; ALGORITHMS
- Publication
Computational Mathematics & Mathematical Physics, 2020, Vol 60, Issue 4, p545
- ISSN
0965-5425
- Publication type
Article
- DOI
10.1134/S096554252004003X