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- W2063455823 abstract "Solutions of conservation laws satisfy the monotonicity property: the number of local extrema is a non-increasing function of time, and local maximum/minimum values decrease/increase monotonically in time. This paper investigates this property from a numerical standpoint. We introduce a class of fully discrete in space and time, high order accurate, difference schemes, called <italic>generalized monotone schemes</italic>. Convergence toward the entropy solution is proven via a new technique of proof, assuming that the initial data has a finite number of extremum values only, and the flux-function is strictly convex. We define <italic>discrete paths of extrema</italic> by tracking local extremum values in the approximate solution. In the course of the analysis we establish the <italic>pointwise convergence</italic> of the trace of the solution along a path of extremum. As a corollary, we obtain a proof of convergence for a MUSCL-type scheme that is second order accurate away from sonic points and extrema." @default.
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- W2063455823 date "1999-02-13" @default.
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- W2063455823 title "Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions" @default.
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- W2063455823 doi "https://doi.org/10.1090/s0025-5718-99-01062-5" @default.
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