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

LSCM with Gaussian points

Abstract

The paper addresses new hp-version of the least-squares collocation method (hp-LSCM) at 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.