Numerical Computation of Brinkman Flow with Stable Mixed Element Method

Abstract EN

Herein, we discuss a mixed finite element method applied to the Brinkman equation of fluid motion in porous medium, which covers a field of situation from the Darcy equation to the Stokes problem associated with various perturbation parameters.

The finite element based on staggered meshes is shown to be stable and effective with each case as the corresponding error estimates for both velocity and pressure are established.

Finally, we present numerical examples confirming the theoretical analysis and the stability of the finite spaces approximation.