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arXiv · 2410.17663

Error analysis of the Monte Carlo method for compressible magnetohydrodynamics

Eduard Feireisl·Maria Lukacova-Medvidova·Bangwei She·Yuhuan Yuan
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Abstract

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.

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Eduard Feireisl, Maria Lukacova-Medvidova, Bangwei She, Yuhuan Yuan. 2024-10-23. Error analysis of the Monte Carlo method for compressible magnetohydrodynamics. https://arxiv.org/abs/2410.17663

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