Abstract:Numerical simulations are carefully-written programs, and their correctness is based on mathematical results. Nevertheless, those programs rely on floating-point arithmetic and the corresponding round-off errors are often ignored. This article deals with a specific simple scheme applied to advection, that is a particular equation from hydrodynamics dedicated to the transport of a substance. It shows a tight bound on the round-off error of the 1D and 2D upwind scheme, with an error roughly proportional to the n… Show more
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