Multi-level Monte Carlo Finite Difference Methods for Fractional Conservation Laws with Random Data

10/01/2020 ∙ by Ujjwal Koley, et al. ∙ 0

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 the solution uncertainty, we design a multi-level Monte Carlo Finite Difference Method (MLMC-FDM) to approximate the ensemble average of the random entropy solutions. Furthermore, we analyze the convergence rates for MLMC-FDM and compare it with the convergence rates for the deterministic case. Additionally, we formulate error vs. work estimates for the multi-level estimator. Finally, we present several numerical experiments to demonstrate the efficiency of these schemes and validate the theoretical estimates obtained in this work.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.