Resolución de las Ecuaciones de Stokes por Mínimos Cuadrados Móviles

Abstract

In this paper a numerical solution fur incompressible stokes equations using moving-least square's interpolant is developed. This approach does not require an element discretization, just a cloud of points is necessary. That possibility is very attractive to be used fur 3-D problems
and defurmable domains.
First, we derivate a variational weak principle for equilibrium equations that include incompressibility restriction and Dirichlet boundary conditions. These conditions are not applicable a posteriori as in Finite Elements. Then the discretizated resultant equations using a MCM interpolant for velocity and pressure fields are presented. Finally, the influence of interpolation on stability is studied.
Numerical and analytical examples are compared, and diffurent aspects of numerical approximation is discussed: number of points, cuadrature order, boundary conditions and accuracy of resuts