Robust globally divergence-free weak Galerkin methods for stationary incompressible convective Brinkman-Forchheimer equations

This paper develops a class of robust weak Galerkin methods for the 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