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Stable approximation of the advection-diffusion equation using the invariant measure

Abstract

We consider an advection-diffusion equation that is both non-coercive and advection-dominated. We present a possible numerical approach, to our best knowledge new, and based on the invariant measure associated to the original equation. The approach has been summarized in [C. Le Bris, F. Legoll and F. Madiot, C. R. Acad. Sci. Paris, Serie I, vol. 354, 799-803 (2016)]. We show that the approach allows for an unconditionally well-posed finite element approximation. We provide a numerical analysis and a set of comprehensive numerical tests showing that the approach can be stable, as accurate as, and more robust than a classical stabilization approach.

Dates and versions

hal-01367417 , version 1 (16-09-2016)

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Claude Le Bris, Frédéric Legoll, François Madiot. Stable approximation of the advection-diffusion equation using the invariant measure. 2017. ⟨hal-01367417⟩
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