A mixed finite element method for the stochastic Boussinesq equations with multiplicative noise
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911337707208704 |
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| author | Vo, Liet |
| author_facet | Vo, Liet |
| contents | This work investigates a fully discrete mixed finite element method for the stochastic Boussinesq system driven by multiplicative noise. The spatial discretization is performed using a standard mixed finite element method, while the temporal discretization is based on a semi-implicit Euler-Maruyama scheme. By combining a localization technique with high-moment stability estimates, we establish error bounds for the velocity, pressure, and temperature approximations. As a direct consequence, we prove convergence in probability for the fully discrete method in both $L^2$ and $H^1$-type norms. Several numerical experiments are presented to validate the theoretical error estimates and demonstrate the effectiveness of the proposed scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21297 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A mixed finite element method for the stochastic Boussinesq equations with multiplicative noise Vo, Liet Numerical Analysis This work investigates a fully discrete mixed finite element method for the stochastic Boussinesq system driven by multiplicative noise. The spatial discretization is performed using a standard mixed finite element method, while the temporal discretization is based on a semi-implicit Euler-Maruyama scheme. By combining a localization technique with high-moment stability estimates, we establish error bounds for the velocity, pressure, and temperature approximations. As a direct consequence, we prove convergence in probability for the fully discrete method in both $L^2$ and $H^1$-type norms. Several numerical experiments are presented to validate the theoretical error estimates and demonstrate the effectiveness of the proposed scheme. |
| title | A mixed finite element method for the stochastic Boussinesq equations with multiplicative noise |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2512.21297 |