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arXiv · 2401.15470

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

X. J. Wang·X. P. Xie
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Abstract

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 $m\ (m\geq1)$ 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

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X. J. Wang, X. P. Xie. 2024-01-27. Robust globally divergence-free weak Galerkin methods for stationary incompressible convective Brinkman-Forchheimer equations. https://arxiv.org/abs/2401.15470

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