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Multilevel Monte-Carlo front tracking for random scalar conservation laws

by N. H. Risebro and Ch. Schwab and F. Weber

(Report number 2012-17)

Abstract
We consider random scalar hyperbolic conservation laws (RSCLs) in spatial dimension $d\ge 1$ with bounded random flux functions which are $P$-a.s. Lipschitz continuous with respect to the state variable, for which there exists a unique random entropy solution (i.e., a measurable mapping from the probability space into $C(0,T;L^1(R^d))$ with finite second moments). We present a convergence analysis of a Multi-Level Monte-Carlo Front-Tracking (MLMCFT) algorithm. Due to the first order convergence of front tracking, we obtain an improved complexity estimate in one space dimension.

Keywords:

@Techreport{RSW12_460,
  author = {N. H. Risebro and Ch. Schwab and F. Weber},
  title = {Multilevel Monte-Carlo front tracking for random scalar conservation laws},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2012-17},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2012/2012-17.pdf },
  year = {2012}
}

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