Error analysis of the Monte Carlo method for compressible magnetohydrodynamics

2024/10/23 by Eduard Feireisl, Mária Lukáčová-Medviďová, Feireisl, Eduard +5
Engineering · Mathematics · #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2410.17663

openalex publication_date 2024/10/23 · openalex created_date 2024/11/13 · openalex updated_date 2026/07/28

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.

Related

• Convergence and error analysis of compressible fluid flows with random data: Monte Carlo method
• Convergence analysis of the Monte Carlo method for random Navier--Stokes--Fourier system
• A Penalty-projection based Efficient and Accurate Stochastic Collocation Method for Magnetohydrodynamic Flows
• An efficient algorithm for simulating ensembles of parameterized MHD flow problems
• Optimal error estimates of a Crank--Nicolson finite element projection method for magnetohydrodynamic equations