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Some results on uniformly high-order accurate essentially nonoscillatory schemes. (English) Zbl 0627.65101
The authors show how to construct for systems of conservation laws essentially nonoscillatory schemes which are uniformly high-order accurate (in the sense of global error for smooth solutions) to any finite order. The main goal of the paper is that, if the initial data \(V_ 0(x)\) are piecewise smooth, then for h sufficiently small \[ TV(V_ h(\cdot,t+\Delta t))\leq TV(V_ h(\cdot,t))+O(h^{N+1}) \] where N is the order of accuracy of the scheme and TV means total variation.
Reviewer: P.I.Ialamov

MSC:
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
Software:
HLLE
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