Research reports

Years: 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

Sparse Tensor Multi-Level Monte Carlo Finite Volume Methods for hyperbolic conservation laws with random intitial data

by Ch. Schwab and S. Mishra

(Report number 2010-24)

Abstract
We consider scalar hyperbolic conservation laws in several (d \ge 1) spatial dimensions with stochastic initial data. We prove existence and uniqueness of a random-entropy solution and show existence of statistical moments of any order k of this random entropy solution. We present a class of numerical schemes of multi-level Monte Carlo Finite Volume (MLMC-FVM) type for the approximation of random entropy solutions as well as of their k-point correlation functions. These schemes are shown to obey the same accuracy vs. work estimate as a single application of the finite volume solver for the corresponding deterministic problem. Numerical experiments demonstrating the efficiency of these schemes are presented. Statistical moments of discontinuous solutions are found to be more regular than pathwise solutions.

Keywords:

@Techreport{SM10_76,
  author = {Ch. Schwab and S. Mishra},
  title = {Sparse Tensor Multi-Level Monte Carlo Finite Volume Methods for hyperbolic conservation laws with random intitial data},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2010-24},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2010/2010-24.pdf },
  year = {2010}
}

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).