13th International Workshop on Variational Multiscale and Stabilized Finite Elemements (VMS 18) - Abstract

Blank, Laura

A robust finite element method for the Brinkman problem

This talk is concerned with the numerical simulation of fluid flow through porous media. The model of interest, the Brinkman model, enables the transition between the Darcy model and the Stokes model. In order to create a robust finite element method, stabilized equal-order elements together with weakly imposed essential boundary conditions are considered. Here, the focus is on a low-order approach such that element-wise linear polynomials are chosen for the velocity space as well as for the pressure space and the penalty-free non-symmetric Nitsche method is employed in order to handle the boundary conditions. Focusing on the two-dimensional case, the resulting robust finite element formulation can be proven to be unconditionally stable and yields optimal a priori error estimates in a mesh-dependent norm [1].

References
[1] Blank, L., Caiazzo, A., Chouly, F., Lozinski, A. and Mura, J.: Analysis of a stabilized penalty-free Nitsche method for the Brinkman, Stokes, and Darcy problems, WIAS Preprint 2489, In ESAIM: Mathematical Modelling and Numerical Analysis accepted (2018).