Robust globally divergence-free weak Galerkin methods for stationary incompressible convective Brinkman-Forchheimer equations
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914655865143296 |
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| author | Wang, X. J. Xie, X. P. |
| author_facet | Wang, X. J. Xie, X. P. |
| contents | 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 |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15470 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Robust globally divergence-free weak Galerkin methods for stationary incompressible convective Brinkman-Forchheimer equations Wang, X. J. Xie, X. P. Numerical Analysis 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 |
| title | Robust globally divergence-free weak Galerkin methods for stationary incompressible convective Brinkman-Forchheimer equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2401.15470 |