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Optimal and near-optimal advection-diffusion finite-difference schemes. V: Error propagation. (English) Zbl 1058.65093

Summary: The wave concept of group (or energy) velocity is used to predict how errors propagate in three numerical schemes for the solution of the diffusion equation with flow and decay. A five-point filter is used to isolate the long and the saw-tooth grid-scale errors. Contour plots are presented which illustrate the markedly different propagation of the long and saw-tooth errors. The energy of long errors is carried downstream with the flow. An illustrative example is given for which, as predicted, the saw-tooth errors go upstream.
Part IV, cf. ibid. 457, No. 2005, 45–65 (2001; Zbl 1049.65086).

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76M20 Finite difference methods applied to problems in fluid mechanics
76R50 Diffusion

Citations:

Zbl 1049.65086
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