The Generalized Stability and Convergence Estimations of Finite Element Methods for the Navier–Stokes Equations

We consider the following “velocity – pressure” formulation of the stationary Navier – Stokes equations: (1.1) − v Δ u → + ∑ j = 1 n ∂ u → ∂ x j + ∇ λ = f ^ ,   x → ∈ Ω https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq5077.tif"/> (1.2) div   u ⇀ = 0 ,   x ⇀ ∈ Ω https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq5078.tif"/> (1.3) u ⇀ = 0 ,   x ⇀ ∈ ∂ Ω https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq5079.tif"/>