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Numerical methods for conservation laws with discontinuous coefficients

by S. Mishra

(Report number 2016-57)

Abstract
Conservation laws with discontinuous coefficients, such as fluxes and source terms, arise in a large number of problems in physics and engineering. We review some recent developments in the theory and numerical methods for these problems. The well-posedness theory for one-dimensional scalar conservation laws is briefly described, with a particular focus on the existence of infinitely many \(L^1\) stable semi-groups of solutions. We also present both aligned and staggered versions of finite volume methods to approximate systems of conservation laws with discontinuous flux. We conclude with some illustrative numerical experiments and a set of open questions.

Keywords: Conservation laws, discontinuous coefficients, entropy solutions, finite difference methods.

@Techreport{M16_694,
  author = {S. Mishra},
  title = {Numerical methods for conservation laws with discontinuous coefficients},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2016-57},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2016/2016-57.pdf },
  year = {2016}
}

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