Computational mathematics

Hp-version of the least-squares collocation method with Gaussian points

L. S. Bryndin, V. A. Belyaev

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

Abstract: 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.

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

UDC: 519.632.4, 519.635.1, 539.3

MSC: 65N35,74K20

Received February 5, 2024, published December 4, 2024

DOI: 10.33048/semi.2024.21.078