Convergence analysis of decoupled mixed FEM for the Cahn-Hilliard-Navier-Stokes equations
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916808376713216 |
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| author | Gao, Haijun Li, Xi Feng, Minfu |
| author_facet | Gao, Haijun Li, Xi Feng, Minfu |
| contents | We develop a decoupled, first-order, fully discrete, energy-stable scheme for the Cahn-Hilliard-Navier-Stokes equations. This scheme calculates the Cahn-Hilliard and Navier-Stokes equations separately, thus effectively decoupling the entire system. To further separate the velocity and pressure components in the Navier-Stokes equations, we use the pressure-correction projection method. We demonstrate that the scheme is primitively energy stable and prove the optimal $L^2$ error estimate of the fully discrete scheme in the $P_r\times P_r\times P_r\times P_{r-1}$ finite element spaces, where the phase field, chemical potential, velocity and pressure satisfy the first-order accuracy in time and the $\left(r+1,r+1,r+1,r\right)th$-order accuracy in space, respectively. Furthermore, numerical experiments are conducted to support these theoretical findings. Notably, compared to other numerical schemes, our algorithm is more time-efficient and numerically shown to be unconditionally stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence analysis of decoupled mixed FEM for the Cahn-Hilliard-Navier-Stokes equations Gao, Haijun Li, Xi Feng, Minfu Numerical Analysis We develop a decoupled, first-order, fully discrete, energy-stable scheme for the Cahn-Hilliard-Navier-Stokes equations. This scheme calculates the Cahn-Hilliard and Navier-Stokes equations separately, thus effectively decoupling the entire system. To further separate the velocity and pressure components in the Navier-Stokes equations, we use the pressure-correction projection method. We demonstrate that the scheme is primitively energy stable and prove the optimal $L^2$ error estimate of the fully discrete scheme in the $P_r\times P_r\times P_r\times P_{r-1}$ finite element spaces, where the phase field, chemical potential, velocity and pressure satisfy the first-order accuracy in time and the $\left(r+1,r+1,r+1,r\right)th$-order accuracy in space, respectively. Furthermore, numerical experiments are conducted to support these theoretical findings. Notably, compared to other numerical schemes, our algorithm is more time-efficient and numerically shown to be unconditionally stable. |
| title | Convergence analysis of decoupled mixed FEM for the Cahn-Hilliard-Navier-Stokes equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2502.14559 |