Workshop on Numerical Methods and Analysis in CFD - Abstract

Gomes, Sonia

A multiscale hybrid-mixed model for Stokes--Brinkman--Darcy flows with divergence-compatible velocity-pressure elements

The current proposal extends a multiscale hybrid-mixed finite element approach, recently considered for Darcy's flows, to the whole range of Stokes and Brinkman problems. Based on divergence-compatible velocity-pressure finite elements in H(div) x L2, the formulation characterizes the approximate solution in terms of components given by well-posed global-local systems, which are subordinated to a partition of the flow domain by general subregions. Hybridization occurs by the introduction of new variables defined over the subregion boundaries (mesh skeleton): tangential traction multiplier (to weakly enforce tangential velocity continuity) and the velocity normal trace (making the H(div)-conforming inter-element connection). The finite element pair of spaces used in the subregions may have richer internal resolution than the boundary normal trace and traction multiplier. Stability of the method is ensured by the divergence compatibility property of velocity and pressure approximations and by a proper choice of the finite element space for the traction variable. Numerical results shall be presented for the verification of the main properties of the method.
This is a joint work with P.G.S. Carvalho and P.R.B. Devloo.