Error analysis of the Monte Carlo method for compressible magnetohydrodynamics
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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_ | 1866914985638100992 |
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| author | Feireisl, Eduard Lukacova-Medvidova, Maria She, Bangwei Yuan, Yuhuan |
| author_facet | Feireisl, Eduard Lukacova-Medvidova, Maria She, Bangwei Yuan, Yuhuan |
| contents | We study random compressible viscous magnetohydrodynamic flows. Combining the Monte Carlo method with a deterministic finite volume method we solve the random system numerically. Quantitative error estimates including statistical and deterministic errors are analyzed up to a stopping time of the exact solution. On the life-span of an exact strong solution we prove the convergence of the numerical solutions. Numerical experiments illustrate rich dynamics of random viscous compressible magnetohydrodynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17663 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Error analysis of the Monte Carlo method for compressible magnetohydrodynamics Feireisl, Eduard Lukacova-Medvidova, Maria She, Bangwei Yuan, Yuhuan Numerical Analysis We study random compressible viscous magnetohydrodynamic flows. Combining the Monte Carlo method with a deterministic finite volume method we solve the random system numerically. Quantitative error estimates including statistical and deterministic errors are analyzed up to a stopping time of the exact solution. On the life-span of an exact strong solution we prove the convergence of the numerical solutions. Numerical experiments illustrate rich dynamics of random viscous compressible magnetohydrodynamics. |
| title | Error analysis of the Monte Carlo method for compressible magnetohydrodynamics |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2410.17663 |