A Local Discontinuous Galerkin approximation for the $p$-Navier-Stokes system, Part III: Convergence rates for the pressure

Abstract

In the present paper, we prove convergence rates for the pressure of the Local Discontinuous Galerkin (LDG) approximation, proposed in Part I of the paper, of systems of $p$-Navier-Stokes type and $p$-Stokes type with $p\in (2,\infty )$. The results are supported by numerical experiments.

arXiv comment18 pages, 0 figures, 1 table, this article is the third part of arXiv:2208.04106 and strongly refers to the second part arXiv:2208.04107