Some results on uniformly high-order accurate essentially nonoscillatory schemes (Q1092631)

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.