Convergence of finite difference schemes for conservation laws in several space dimensions: the corrected antidiffusive flux approach
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- by Frédéric Coquel and Philippe LeFloch PDF
- Math. Comp. 57 (1991), 169-210 Request permission
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.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Math. Comp. 57 (1991), 169-210
- MSC: Primary 65M06; Secondary 35L65, 76L05, 76M20
- DOI: https://doi.org/10.1090/S0025-5718-1991-1079010-2
- MathSciNet review: 1079010