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Numerical methods for conservation laws with discontinuous coefficients. (English) Zbl 1368.65156
Abgrall, Rémi (ed.) et al., Handbook on numerical methods for hyperbolic problems. Applied and modern issues. Amsterdam: Elsevier/North Holland (ISBN 978-0-444-63910-3/hbk; 978-0-444-63911-0/ebook). Handbook of Numerical Analysis 18, 479-506 (2017).
Summary: 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 semigroups 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.
For the entire collection see [Zbl 1364.65001].

MSC:
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
35R05 PDEs with low regular coefficients and/or low regular data
76S05 Flows in porous media; filtration; seepage
76M12 Finite volume methods applied to problems in fluid mechanics
90B20 Traffic problems in operations research
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