Optimal error estimates for a fully discrete, highly efficient decoupled scheme for the 2D/3D diffuse interface two-phase MHD flows
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917343759695872 |
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| author | Zhang, Ke Su, Haiyan |
| author_facet | Zhang, Ke Su, Haiyan |
| contents | In this paper, we derive optimal L2- and H1-norm error estimates for a fully discrete convex-splitting decoupled finite element method (FEM) for the two-phase diffuse interface magnetohydrodynamics (MHD) system. We use the semi-implicit backward Euler scheme in time and employ the standard inf-sup stable Taylor--Hood or Mini elements to discretize the velocity and pressure. Furthermore, we apply a pressure-correction scheme to decouple the velocity from the pressure. The optimal error estimates are obtained via novel Ritz and Stokes quasi-projection techniques. In addition, the unconditional energy stability of the proposed scheme is ensured. Numerical examples are presented to validate the theoretical analysis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_14656 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal error estimates for a fully discrete, highly efficient decoupled scheme for the 2D/3D diffuse interface two-phase MHD flows Zhang, Ke Su, Haiyan Numerical Analysis In this paper, we derive optimal L2- and H1-norm error estimates for a fully discrete convex-splitting decoupled finite element method (FEM) for the two-phase diffuse interface magnetohydrodynamics (MHD) system. We use the semi-implicit backward Euler scheme in time and employ the standard inf-sup stable Taylor--Hood or Mini elements to discretize the velocity and pressure. Furthermore, we apply a pressure-correction scheme to decouple the velocity from the pressure. The optimal error estimates are obtained via novel Ritz and Stokes quasi-projection techniques. In addition, the unconditional energy stability of the proposed scheme is ensured. Numerical examples are presented to validate the theoretical analysis. |
| title | Optimal error estimates for a fully discrete, highly efficient decoupled scheme for the 2D/3D diffuse interface two-phase MHD flows |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2511.14656 |