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Convergence of MUSCL and filtered schemes for scalar conservation laws and Hamilton-Jacobi equations

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Summary.

This paper considers the questions of convergence of: (i) MUSCL type (i.e. second-order, TVD) finite-difference approximations towards the entropic weak solution of scalar, one-dimensional conservation laws with strictly convex flux and (ii) higher-order schemes (filtered to ``preserve'' an upper-bound on some weak second-order finite differences) towards the viscosity solution of scalar, multi-dimensional Hamilton-Jacobi equations with convex Hamiltonians.

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Authors and Affiliations

  1. Ceremade, Universit\'e Paris--Dauphine, Place de Lattre de Tassigny, F-75775 Paris, Cedex 16, France , , , , , , FR

    P.-L. Lions

  2. Department of Mathematics, University of Wisconsin -- Madison, Madison, WI 53706, USA , , , , , , US

    P.E. Souganidis

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  1. P.-L. Lions
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  2. P.E. Souganidis
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Received May 16, 1994

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Lions, PL., Souganidis, P. Convergence of MUSCL and filtered schemes for scalar conservation laws and Hamilton-Jacobi equations . Numer. Math. 69, 441–470 (1995). https://doi.org/10.1007/s002110050102

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  • DOI: https://doi.org/10.1007/s002110050102

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