English

On a robust inf-sup condition for the Stokes problem in slender domains -- with application to preconditioning

Numerical Analysis 2025-10-29 v1 Numerical Analysis Analysis of PDEs

Abstract

We identify a norm on the pressure variable in the Stokes equation that allows us to prove a continuous inf-sup condition with a constant independent of the domain's aspect ratio. This is in contrast to the standard inf-sup constant, which breaks down as the aspect ratio increases. We further apply our result to construct robust operator preconditioners for the Stokes problem in slender domains. Several numerical examples illustrate the theory.

Keywords

Cite

@article{arxiv.2510.24590,
  title  = {On a robust inf-sup condition for the Stokes problem in slender domains -- with application to preconditioning},
  author = {Espen Sande and Timo Koch and Miroslav Kuchta and Kent-Andre Mardal},
  journal= {arXiv preprint arXiv:2510.24590},
  year   = {2025}
}