Robust Globally Divergence-Free Weak Galerkin Methods for Stationary Incompressible Convective Brinkman-Forchheimer Equations
Year: 2024
Author: Xiaojuan Wang, Xiaoping Xie
Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 4 : pp. 956–995
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2024-0007
Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 4 : pp. 956–995
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 40
Keywords: Brinkman-Forchheimer equations weak Galerkin method divergence-free error estimate.
Author Details
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Robust globally divergence-free weak Galerkin methods for unsteady incompressible convective Brinkman–Forchheimer equations
Wang, Xiaojuan
Xiao, Jihong
Xie, Xiaoping
Zhang, Shiquan
Communications in Nonlinear Science and Numerical Simulation, Vol. 143 (2025), Iss. P.108578
https://doi.org/10.1016/j.cnsns.2024.108578 [Citations: 0]