Continuous/Discontinuous Finite Element Approximation of a 2d Navier-Stokes Problem Arising in Fluid Confinement

Abstract

In this work, a stationary 2d Navier-Stokes problem with nonlinear feedback forces field is considered in the stream-function formulation. We use the Continuous/Discontinuous Finite Element Method (CD-FEM), with interior penalty terms, to numerically solve the associated boundary-value problem. For the associated continuous and discrete problems, we prove the existence of weak solutions and establish the conditions for their uniqueness. Consistency, stability and convergence of the method are also shown analytically. To validate the numerical model regarding its applicability and robustness, several test cases are carried out.