On the inf-sup condition in slender geometries – mixed dimensions and application to brain fluid dynamics
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The inf-sup constant degenerates in slender geometry as it is related to the aspect-ratio of the geometry. In simulations of cerebrospinal fluid flow within and around the brain the condition number of the preconditioned system, when preconditioned with block preconditioner with good performance on unit sized geometries, are in the order of 10^5-10^6 [1] due to the complicated geometries. Here we will discuss how the inf-sup condition, even in the continuous case, in a mixed dimensional setting is robust with respect to the aspect-ratio of the domain and show how this may be utilized for constructing geometry robust preconditioners.