On the full space--time discretization of the generalized Stokes equations: The Dirichlet case

TL;DR

This paper analyzes the space-time discretization of generalized Stokes equations with Dirichlet boundary conditions, providing error estimates that are robust against degeneracy parameters and achieving optimal convergence rates for certain cases.

Contribution

It introduces error estimates for the discretization of generalized Stokes equations that are independent of degeneracy parameters and establishes optimal convergence rates for specific p-values.

Findings

Error estimates are independent of the degeneracy parameter δ.

Optimal convergence rates are achieved for p ≤ 2.

The analysis applies to a broad range of p in [2d/(d+2), ∞).

Abstract

In this work we treat the space-time discretization of the generalized Stokes equations in the case of Dirichlet boundary conditions. We prove error estimates in the case $p\in[\frac{2d}{d+2},\infty)$ that are independent of the degeneracy parameter $\delta\in[0,\delta_0]$. For $p\leq 2$, our convergence rate is optimal.