Analysis of an iterative method for variable density incompressible fluids

Abstract

We derive error bounds for an iterative method used by Okamoto to prove the existence of strong solutions for the equations of nonhomogeneous incompressible fluids.

A convergent post-processed discontinuous Galerkin method for incompressible flow with variable density

“…For smooth initial value satisfying the positivity condition (1.3), existence and uniqueness of smooth solutions of (1.1) in two dimensions were proved in [8,15,20]. Hence, this problem does not generate shock wave in finite time (at least in 2D).…”

Error analysis of a fully discrete finite element method for variable density incompressible flows in two dimensions

“…We consider (1.1)-(1.3) in a convex polygon Ω ⊂ R 2 up to a given time , with the following boundary and initial conditions: u = 0 on Ω × [0, ], = 0 and u = u 0 at = 0, (1.4) where 0 and u 0 are given functions, and Ω the boundary of the domain Ω. For given smooth initial data 0 and u 0 with positive density, i.e., min the existence and uniqueness of smooth solutions of (1.1)-(1.4) have been proved in [14,32,44]. In particular, this hyperbolic-parabolic system does not generate shock wave (at least in 2D).…”