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

2018/10/30 by Pauly, Dirk, Repin, Sergey
#35J57 #65N15 #76D07 #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1810.12555

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.

Related

• On a robust inf-sup condition for the Stokes problem in slender domains -- with application to preconditioning
• Resolvent Estimates in L^∞ for the Stokes Operator in Nonsmooth Domains
• Justification of lubrication approximation: an application to fluid/solid interactions
• Stokes Resolvent Estimates in Spaces of Bounded Functions
• A note on the pressure of strong solutions to the Stokes system in bounded and exterior domains