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Accurate numerical schemes for approximating intitial-boundary value problems for systems of conservation law

by S. Mishra and L. V. Spinolo

(Report number 2011-57)

Abstract
Solutions of initial-boundary value problems for systems of conservation laws depend on the underlying viscous mechanism, namely different viscosity operators lead to different limit solutions. Standard numerical schemes for approximating conservation laws do not take into account this fact and converge to solutions that are not necessarily physically relevant. We design numerical schemes that incorporate explicit information about the underlying viscosity mechanism and approximate the physically relevant solution. Numerical experiments illustrating the robust performance of these schemes are presented.

Keywords:

@Techreport{MS11_109,
  author = {S. Mishra and L. V. Spinolo},
  title = {Accurate numerical schemes for approximating intitial-boundary value problems for systems of conservation law},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2011-57},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2011/2011-57.pdf },
  year = {2011}
}

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