Вычислительная математика

Hp-вариант метода коллокации и наименьших квадратов с уравнениями коллокации в корнях полиномов Лежандра

Л. С. Брындин, В. А. Беляев

Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences, Institutskaya str., 4/1, 630090, Novosibirsk, Russia

Аннотация: The paper addresses new hp-version of the least-squares collocation method (hp-LSCM) with Gaussian points. The optimal order of convergence of the developed method for solving boundary value problems for Poisson's equation, biharmonic equation, and for a system of partial differential equations of the Reissner–Mindlin plate problem is shown numerically. An algorithm for obtaining a system of linear algebraic equations with a invertible quadratic matrix in hp-LSCM is given. The advantages of the developed collocation method in comparison with previous versions of the hp-LSCM and isogeometric collocation method are shown.

Ключевые слова: least-squares collocation method, optimal convergence, Gaussian points, Poisson's equation, biharmonic equation, Kirchhoff – Love theory, Reissner – Mindlin theory, plate bending.

УДК: 519.632.4, 519.635.1, 539.3

MSC: 65N35,74K20

Поступила 5 февраля 2024 г., опубликована 4 декабря 2024 г.

DOI: 10.33048/semi.2024.21.078