Robust globally divergence-free weak Galerkin methods for unsteady incompressible convective Brinkman-Forchheimer equations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916457234825216 |
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| author | Wang, Xiaojuan Xiao, Jihong Xie, Xiaoping Zhang, Shiquan |
| author_facet | Wang, Xiaojuan Xiao, Jihong Xie, Xiaoping Zhang, Shiquan |
| contents | This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman-Forchheimer equations. For the spatial discretization, the methods adopt the piecewise polynomials of degrees $m\ (m\geq1)$ and $m-1$ respectively to approximate the velocity and pressure inside the elements, and piecewise polynomials of degree $m$ to approximate their numerical traces on the interfaces of elements. In the fully discrete method, the backward Euler difference scheme is used to approximate the time derivative. The methods are shown to yield globally divergence-free velocity approximation. Optimal a priori error estimates in the energy norm and $L^2$ norm are established. A convergent linearized iterative algorithm is designed for solving the fully discrete system. Numerical experiments are provided to verify the theoretical results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_21289 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Robust globally divergence-free weak Galerkin methods for unsteady incompressible convective Brinkman-Forchheimer equations Wang, Xiaojuan Xiao, Jihong Xie, Xiaoping Zhang, Shiquan Numerical Analysis This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman-Forchheimer equations. For the spatial discretization, the methods adopt the piecewise polynomials of degrees $m\ (m\geq1)$ and $m-1$ respectively to approximate the velocity and pressure inside the elements, and piecewise polynomials of degree $m$ to approximate their numerical traces on the interfaces of elements. In the fully discrete method, the backward Euler difference scheme is used to approximate the time derivative. The methods are shown to yield globally divergence-free velocity approximation. Optimal a priori error estimates in the energy norm and $L^2$ norm are established. A convergent linearized iterative algorithm is designed for solving the fully discrete system. Numerical experiments are provided to verify the theoretical results. |
| title | Robust globally divergence-free weak Galerkin methods for unsteady incompressible convective Brinkman-Forchheimer equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2410.21289 |