Attractors and Error Estimates for Discretizations of Incompressible Navier--Stokes Equations

Authors:
Yin Yan
Affiliations:
-
Venue:
SIAM Journal on Numerical Analysis
Year:
1996

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Long-Term Stability Estimates and Existence of a Global Attractor in a Finite Element Approximation of the Navier-Stokes Equations with Numerical Subgrid Scale Modeling

SIAM Journal on Numerical Analysis

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Abstract

By embedding sets of nodal values to function spaces, variational arguments are applied to the finite difference approximations to the two-dimensional incompressible Navier--Stokes equations. The error estimates for trajectories and the {\it time-free} error estimates with tolerance for attractors are proved. The upper semicontinuity of the attractors with respect to the finite difference discretizations are also proved. Arguments of applying the techniques to the finite element approximations are also given.