Research reports

Years: 2025 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Numerical approximation of statistical solutions of scalar conservation laws

by U. S. Fjordholm and K. Lye and S. Mishra

(Report number 2017-52)

Abstract
We propose efficient numerical algorithms for approximating statistical solutions of scalar conservation laws. The proposed algorithms combine finite volume spatio-temporal approximations with Monte Carlo and multi-level Monte Carlo discretizations of the probability space. Both sets of methods are proved to converge to the entropy statistical solution. We also prove that there is a considerable gain in efficiency resulting from the multi-level Monte Carlo method over the standard Monte Carlo method. Numerical experiments illustrating the ability of both methods to accurately compute multi-point statistical quantities of interest are also presented.

Keywords: Hyperbolic systems, statistical solutions, probability measures, Wasserstein Metric

@Techreport{FLM17_748,
  author = {U. S. Fjordholm and K. Lye and S. Mishra},
  title = {Numerical approximation of statistical solutions of scalar conservation laws},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2017-52},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2017/2017-52.pdf },
  year = {2017}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).