A note on the uniform inf-sup condition for the Brinkman problem in highly heterogeneous media

摘要

In this short note we study the interpolation spaces based uniform inf-sup condition for Brinkman equation in highly heterogeneous domains. The result is known to hold in the case of a uniform constant permeability. Our numerical construction and experiments show that it is not true for the Taylor-Hood and the Mini elements applied to problems with highly heterogeneous coefficients.