Divergence-free decoupled finite element methods for incompressible flow problems
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918233844482048 |
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| author | John, Volker Li, Xu Merdon, Christian |
| author_facet | John, Volker Li, Xu Merdon, Christian |
| contents | Incompressible flows are modeled by a coupled system of partial differential equations for velocity and pressure, Starting from a divergence-free mixed method proposed in [John, Li, Merdon and Rui, Math. Models Methods Appl. Sci. 34(05):919--949, 2024], this paper proposes $\vecb{H}(\mathrm{div})$-conforming finite element methods which decouple the velocity and pressure by constructing divergence-free basis functions. Algorithmic issues like the computation of this basis and the imposition of non-homogeneous Dirichlet boundary conditions are discussed. Numerical studies at two- and three-dimensional Stokes problems compare the efficiency of the proposed methods with methods from the above mentioned paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05642 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Divergence-free decoupled finite element methods for incompressible flow problems John, Volker Li, Xu Merdon, Christian Numerical Analysis 76D07, 76M10, 65M60 Incompressible flows are modeled by a coupled system of partial differential equations for velocity and pressure, Starting from a divergence-free mixed method proposed in [John, Li, Merdon and Rui, Math. Models Methods Appl. Sci. 34(05):919--949, 2024], this paper proposes $\vecb{H}(\mathrm{div})$-conforming finite element methods which decouple the velocity and pressure by constructing divergence-free basis functions. Algorithmic issues like the computation of this basis and the imposition of non-homogeneous Dirichlet boundary conditions are discussed. Numerical studies at two- and three-dimensional Stokes problems compare the efficiency of the proposed methods with methods from the above mentioned paper. |
| title | Divergence-free decoupled finite element methods for incompressible flow problems |
| topic | Numerical Analysis 76D07, 76M10, 65M60 |
| url | https://arxiv.org/abs/2512.05642 |