On the full space--time discretization of the generalized Stokes equations: The Dirichlet case
arXiv:1610.063201.211 citationsh-index: 33
Originality Synthesis-oriented
AI Analysis
Provides rigorous numerical analysis for a class of PDEs relevant to fluid dynamics, but the result is incremental as it extends existing techniques to a specific parameter range.
The authors prove error estimates for the space-time discretization of the generalized Stokes equations with Dirichlet boundary conditions, achieving optimal convergence rates for p ≤ 2 and estimates independent of the degeneracy parameter δ.
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 $δ\in[0,δ_0]$. For $p\leq 2$, our convergence rate is optimal.