Numerics and hydrodynamic stability: toward error control in computational fluid dynamics

We critically review the available error analysis in computational fluid dynamics (CFD) and come to the conclusion that the existing error estimates are meaningless in most cases of interest. We propose a new approach to error analysis in CFD aiming at reliable and efficient adaptive quantitative error control. This is based on a precise analysis of hydrodynamic stability coupled with Galerkin orthogonality. We prove a priori- and a posteriori-type error estimates in a model case for pipe flow, formulate corresponding adaptive algorithms, and discuss the potential of this approach for adaptive error control in CFD.

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