2020/10/01 by Ujjwal Koley, Koley, Ujjwal, Deep Ray +3
Engineering · Environmental Science · Mathematics · #35L65 #65C05 #65M06 #65M12 #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Fractional Differential Equations Solutions #G.1.8 #G.3 #Hydrology and Drought Analysis #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2010.00537
openalex publication_date 2020/10/01 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We establish a notion of random entropy solution for degenerate fractional\nconservation laws incorporating randomness in the initial data, convective flux\nand diffusive flux. In order to quantify the solution uncertainty, we design a\nmulti-level Monte Carlo Finite Difference Method (MLMC-FDM) to approximate the\nensemble average of the random entropy solutions. Furthermore, we analyze the\nconvergence rates for MLMC-FDM and compare it with the convergence rates for\nthe deterministic case. Additionally, we formulate error vs. work estimates for\nthe multi-level estimator. Finally, we present several numerical experiments to\ndemonstrate the efficiency of these schemes and validate the theoretical\nestimates obtained in this work.\n