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Convergence of the Piecewise Linear Approximation and Collocation Method for a Hypersingular Integral Equation on a Closed Surfaceстатья
Информация о цитировании статьи получена из
Web of Science
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 12 февраля 2018 г.
- Авторы: Setukha A.V., Semenova A.V.
- Журнал: Differential Equations
- Том: 53
- Номер: 9
- Год издания: 2017
- Издательство: Pleiades Publishing, Inc.
- Местоположение издательства: New York, USA
- Первая страница: 1231
- Последняя страница: 1246
- DOI: 10.1134/S0012266117090129
- Аннотация: We study the numerical solution of a linear hypersingular integral equation arising when solving the Neumann boundary value problem for the Laplace equation by the boundary integral equation method with the solution represented in the form of a double layer potential. The integral in this equation is understood in the sense of Hadamard finite value. We construct quadrature formulas for the integral occurring in this equation based on a triangulation of the surface and an application of the linear approximation to the unknown function on each of the triangles approximating the surface. We prove the uniform convergence of the quadrature formulas at the interpolation nodes as the triangulation size tends to zero. A numerical solution scheme for this integral equation based on the suggested quadrature formulas and the collocation method is constructed. Under additional assumptions about the shape of the surface, we prove a uniform estimate for the error in the numerical solution at the interpolation nodes.
- Добавил в систему: Сетуха Алексей Викторович