TY - JOUR
T1 - Robust Globally Divergence-Free Weak Galerkin Methods for Stationary Incompressible Convective Brinkman-Forchheimer Equations
AU - Wang , Xiaojuan
AU - Xie , Xiaoping
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 956
EP - 995
PY - 2024
DA - 2024/12
SN - 17
DO - http://doi.org/10.4208/nmtma.OA-2024-0007
UR - https://global-sci.org/intro/article_detail/nmtma/23648.html
KW - Brinkman-Forchheimer equations, weak Galerkin method, divergence-free, error estimate.
AB - <p style="text-align: justify;">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.</p>