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

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

Xiaojuan Wang

Xiaoping Xie

  1. 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]