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Accurate numerical schemes for approximating initial-boundary value problems for systems of conservation laws

Siddhartha Mishra

Seminar for Applied Mathematics (SAM), ETH Zurich, Rämistrasse-101, Zurich 8092, Switzerland

Center of Mathematics for Applications (CMA), University of Oslo, Oslo, Norway

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and

Laura V. Spinolo

IMATI-CNR, via Ferrata 1, Pavia, 27100, Italy

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https://doi.org/10.1142/S0219891615500034Cited by:7 (Source: Crossref)

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 physical-viscosity solution. Numerical experiments illustrating the robust performance of these schemes are presented.

Keywords:

AMSC: 65M08, 35L65

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