Uniform-in-time error estimates for spectral Galerkin approximations of a mass diffusion model

Abstract

The goal of this paper is to present uniform-in-time error estimates by considering spectral Galerkin approximations of the Kazhikhov-Smagulov model for strong solutions. To be more precise, we derive an optimal uniform-in-time error bound in the boldsymbol{H}^1\times H^2$ norm for the velocity and density approximations being stated in Theorem 6.