Multilevel Monte Carlo Finite Difference Methods for Fractional Conservation Laws with Random Data
نویسندگان
چکیده
We establish a notion of random entropy solution for degenerate fractional conservation laws incorporating randomness in the initial data, convective flux, and diffusive flux. In order to quantify uncertainty, we design multilevel Monte Carlo finite difference method (MLMC-FDM) approximate ensemble average solutions. Furthermore, analyze convergence rates MLMC-FDM compare them with deterministic case. Additionally, formulate error vs. work estimates estimator. Finally, present several numerical experiments demonstrate efficiency these schemes validate theoretical obtained this work.
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ژورنال
عنوان ژورنال: SIAM/ASA Journal on Uncertainty Quantification
سال: 2021
ISSN: ['2166-2525']
DOI: https://doi.org/10.1137/19m1279447