Convergence of finite difference schemes for conservation laws in several space dimensions: the corrected antidiffusive flux approach

Coquel, Frédéric; LeFloch, Philippe

doi:10.1090/S0025-5718-1991-1079010-2

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Convergence of finite difference schemes for conservation laws in several space dimensions: the corrected antidiffusive flux approach

Authors: Frédéric Coquel and Philippe LeFloch
Journal: Math. Comp. 57 (1991), 169-210
MSC: Primary 65M06; Secondary 35L65, 76L05, 76M20
MathSciNet review: 1079010
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Abstract: In this paper, we apply the general method we have presented elsewhere and prove the convergence of a class of explicit and high-order accurate finite difference schemes for scalar nonlinear hyperbolic conservation laws in several space dimensions. We consider schemes constructed--from an E-scheme-- by the corrected antidiffusive flux approach. We derive "sharp" entropy inequalities satisfied by both E-schemes and the high-order accurate schemes under consideration. These inequalities yield uniform estimates of the discrete space derivatives of the approximate solutions, which are weaker than the so-called BV (i.e., bounded variation) estimates but sufficient to apply our previous theory.

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