The Stationary Stokes Problem in Exterior Domains: Estimates of the Distance to Solenoidal Fields and Functional A Posteriori Error Estimates
This work provides rigorous error estimation tools for the Stokes problem in exterior domains, which is important for numerical analysis and computational fluid dynamics, though the results are incremental and domain-specific.
The paper derives computable estimates for the distance to solenoidal fields and functional a posteriori error estimates for the stationary Stokes problem in exterior domains, providing fully computable majorants for the error between exact and approximate solutions.
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.