On the accuracy of stable schemes for 2D scalar conservation laws

Goodman, Jonathan B.; LeVeque, Randall J.

doi:10.1090/S0025-5718-1985-0790641-4

On the accuracy of stable schemes for $2$D scalar conservation laws
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by Jonathan B. Goodman and Randall J. LeVeque PDF

Math. Comp. 45 (1985), 15-21 Request permission

Abstract:

We show that any conservative scheme for solving scalar conservation laws in two space dimensions, which is total variation diminishing, is at most first-order accurate.

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