Time delay and finite differences for the non‐stationary non‐linear Navier–Stokes equations

摘要

AbstractIn the present paper we use a time delay ϵ>0 for an energy conserving approximation of the non‐linear term of the non‐stationary Navier–Stokes equations. We prove that the corresponding initial‐value problem (Nϵ) in smoothly bounded domainsG⊆ ℝ3is well‐posed. We study a semidiscretized difference scheme for (Nϵ) and prove convergence to optimal order in the Sobolev spaceH2(G). Passing to the limit ϵ→0 we show that the sequence of stabilized solutions has an accumulation point such that it solves the Navier–Stokes problem (No) i