The Stationary Stokes Problem in Exterior Domains: Estimates of the Distance to Solenoidal Fields and Functional A Posteriori Error Estimates

TL;DR

This paper analyzes the stationary Stokes problem in exterior domains, providing explicit estimates of the distance to divergence-free fields and developing computable error bounds for approximate solutions.

Contribution

It introduces fully computable estimates of the distance to solenoidal fields and derives a posteriori error estimates for solutions in exterior domains.

Findings

Explicit constants for stability in exterior domains

Computable bounds for divergence-free field approximation

A posteriori error estimates for Stokes solutions

Abstract

This paper is concerned with the analysis of the inf-sup condition arising in the stationary Stokes problem in exterior domains. We deduce values of the constant in the stability lemma, which yields fully computable estimates of the distance to the set of divergence free fields defined in exterior domains. Using these estimates we obtain computable majorants of the difference between the exact solution of the Stokes problem in exterior domains and any approximation from the admissible (energy) class of functions satisfying the Dirichlet boundary condition exactly.