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Multilevel Monte Carlo front-tracking for random scalar conservation laws

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A Correction to this article was published on 23 August 2017

A Correction to this article was published on 23 August 2017

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Abstract

We consider random scalar hyperbolic conservation laws in spatial dimension \(d\ge 1\) with bounded random flux functions which are Lipschitz continuous with respect to the state variable, for which there exists a unique random entropy solution. We present a convergence analysis of a multilevel Monte Carlo front-tracking algorithm. It is based on “pathwise” application of the front-tracking method for deterministic conservation laws. Due to the first order convergence of front tracking, we obtain an improved complexity estimate in one space dimension.

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Change history

  • 23 August 2017

    A correction to this article has been published.

  • 23 August 2017

    An erratum to this article has been published.

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Acknowledgments

This work is performed as part of ETH interdisciplinary research Grant CH1-03 10-1 and partially supported by NRF-project 214495 LIQCRY. The work of Schwab was supported in part by ERC FP7 Grant No. AdG 247277. The work of Risebro was performed while visiting SAM during a sabbatical in the academic year 2011/2012. The authors thank Jonas Šukys for providing a reference solution for a numerical experiment and Siddhartha Mishra and Jonas Šukys for valuable discussions.

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Authors and Affiliations

  1. Department of Mathematics, University of Oslo, Blindern, P.O. Box 1053, 0316, Oslo, Norway

    Nils Henrik Risebro & Franziska Weber

  2. Seminar for Applied Mathematics, ETH Zürich, ETH Zentrum HG G 57.1, Rämistrasse 101, Zurich, Switzerland

    Christoph Schwab

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  1. Nils Henrik Risebro
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  2. Christoph Schwab
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  3. Franziska Weber
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Correspondence to Nils Henrik Risebro.

Additional information

Communicated by Desmond Higham.

A correction to this article is available online at https://doi.org/10.1007/s10543-017-0670-0.

An erratum to this article is available at https://doi.org/10.1007/s10543-017-0670-0.

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Risebro, N.H., Schwab, C. & Weber, F. Multilevel Monte Carlo front-tracking for random scalar conservation laws. Bit Numer Math 56, 263–292 (2016). https://doi.org/10.1007/s10543-015-0550-4

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