ON THE STABILITY OF THE RESIDUAL-FREE BUBBLES FOR THE NAVIER-STOKES EQUATIONS

Abstract

Abstract:

This paper considers the Galerkin finite element method for the incompressible
Navier-Stokes equations in two dimensions, where the finite-dimensional spaces employed
consist of piecewise polynomials enriched with residual-free bubble (RFB) functions. The
stability features of the residual-free bubble functions for the linearized Navier-Stokes equa-
tions are analyzed in this work. It is shown that the enrichment of the velocity space by
bubble functions stabilizes the numerical method for any value of the viscosity parameter
for triangular elements and for values of the viscosity parameter in the vanishing limit case
for quadrilateral elements.

Key words: Galerkin finite element method, incompressible Navier-Stokes equations, sta-bility

CLC Number:

35Q30

Ali I.Nesliturk. ON THE STABILITY OF THE RESIDUAL-FREE BUBBLES FOR THE NAVIER-STOKES EQUATIONS[J].Acta mathematica scientia,Series B, 2005, 25(4): 715-730.

Trendmd

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