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

2016/09/15 by Claude Le Bris, Bris, Claude Le, Frédéric Legoll +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1609.04777

openalex publication_date 2016/09/15 · openalex created_date 2016/09/30 · openalex updated_date 2026/08/01

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.

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