International Conference «Mathematical and Information Technologies, MIT-2016»

## Idimeshev S. Golushko S.K. Shapeev V.P.## hp-Version of Collocation and Least Residuals Method in Mechanics of Laminated Composite Plates## Reporter: Idimeshev S.
Collocation and least residuals (CLR) method is projection numerical method for solving boundary value problems for partial differential equation. The authors suggest hp-version of CLR method that based on the use of polynomials of higher degrees [1, 2]. The developed hp-version has three major advantages. The method is based on the use of polynomials of higher degrees, written as a direct product of Chebyshev polynomials that helps to minimize the accumulation of rounding errors. Special choice of collocation points, using the roots of Chebyshev polynomials, provides fast convergence and high accuracy of numerical solutions for a wide class of functions. In the CLR method the solution of a corresponding linear algebra problem is defined as the minimum of the functional of residual norm. This brings linear algebra problem well-conditioned. These advantages of hp-version of CLR method allows to carry out calculations at a lower computational cost. To reports list |