Collocation and Least Residuals Method and Its Applications

• Main Author: Shapeev Vasily
• Format: Article
• Language: English
• Published: EDP Sciences 2016-01-01
• Series: EPJ Web of Conferences
• Online Access: http://dx.doi.org/10.1051/epjconf/201610801009

The collocation and least residuals (CLR) method combines the methods of collocations (CM) and least residuals. Unlike the CM, in the CLR method an approximate solution of the problem is found from an overdetermined system of linear algebraic equations (SLAE). The solution of this system is sought under the requirement of minimizing a functional involving the residuals of all its equations. On the one hand, this added complication of the numerical algorithm expands the capabilities of the CM for solving boundary value problems with singularities. On the other hand, the CLR method inherits to a considerable extent some convenient features of the CM. In the present paper, the CLR capabilities are illustrated on benchmark problems for 2D and 3D Navier–Stokes equations, the modeling of the laser welding of metal plates of similar and different metals, problems investigating strength of loaded parts made of composite materials, boundary-value problems for hyperbolic equations.