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Volume 17, Issue 4
Robust Globally Divergence-Free Weak Galerkin Methods for Stationary Incompressible Convective Brinkman-Forchheimer Equations

Xiaojuan Wang & Xiaoping Xie

Numer. Math. Theor. Meth. Appl., 17 (2024), pp. 956-995.

Published online: 2024-12

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  • 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.

  • AMS Subject Headings

65M60, 65N30

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COPYRIGHT: © Global Science Press

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@Article{NMTMA-17-956, author = {Wang , Xiaojuan and Xie , Xiaoping}, title = {Robust Globally Divergence-Free Weak Galerkin Methods for Stationary Incompressible Convective Brinkman-Forchheimer Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2024}, volume = {17}, number = {4}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2024-0007}, url = {http://global-sci.org/intro/article_detail/nmtma/23648.html} }
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 -

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.

Wang , Xiaojuan and Xie , Xiaoping. (2024). Robust Globally Divergence-Free Weak Galerkin Methods for Stationary Incompressible Convective Brinkman-Forchheimer Equations. Numerical Mathematics: Theory, Methods and Applications. 17 (4). 956-995. doi:10.4208/nmtma.OA-2024-0007
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