Robust Globally Divergence-Free Weak Galerkin Methods for Stationary Incompressible Convective Brinkman-Forchheimer Equations

Abstract

This paper develops a class of robust weak Galerkin methods for stationary incompressible convective Brinkman-Forchheimer equations. The methods adopt piecewise polynomials of degrees $m (m ≥ 1)$ and $m−1$ respectively for the approximations of velocity and pressure variables inside the elements and piecewise polynomials of degrees $k $$(k=m−1, m),$ and $m$ respectively for their numerical traces on the interfaces of elements, and are shown to yield globally divergence-free velocity approximation. Existence and uniqueness results for the discrete schemes, as well as optimal a priori error estimates, are established. A convergent linearized iterative algorithm is also presented. Numerical experiments are provided to verify the performance of the proposed methods.