Artículos de revistas
Finite element methods for the Stokes system based on a Zienkiewicz type N-simplex
Fecha
2014-04-09Registro en:
Computer Methods in Applied Mechanics and Engineering, Amsterdam, v. 272, p. 83-99, abr 2014
10.1016/j.cma.2013.12.018
Autor
Buscaglia, Gustavo Carlos
Santos, Vitoriano Ruas de Barros
Institución
Resumen
Hermite interpolation is increasingly showing to be a powerful numerical solution tool, as
applied to different kinds of second order boundary value problems. In this work we present
two Hermite finite element methods to solve viscous incompressible flows problems, in
both two- and three-dimension space. In the two-dimensional case we use the Zienkiewicz
triangle to represent the velocity field, and in the three-dimensional case an extension of
this element to tetrahedra, still called a Zienkiewicz element. Taking as a model the Stokes
system, the pressure is approximated with continuous functions, either piecewise linear or
piecewise quadratic, according to the version of the Zienkiewicz element in use, that is,
with either incomplete or complete cubics. The methods employ both the standard
Galerkin or the Petrov–Galerkin formulation first proposed in Hughes et al. (1986) [18],
based on the addition of a balance of force term. A priori error analyses point to optimal
convergence rates for the PG approach, and for the Galerkin formulation too, at least in
some particular cases. From the point of view of both accuracy and the global number of
degrees of freedom, the new methods are shown to have a favorable cost-benefit ratio,
as compared to velocity Lagrange finite elements of the same order, especially if the Galerkin
approach is employed.