Geodesic
A numerical comparison of some Multiscale Finite Element approaches for advection-dominated problems in heterogeneous media
Le Bris, Claude1  ; Legoll, Frédéric1  ; Madiot, François1 
1 École des Ponts and INRIA, 6 et 8 avenue Blaise Pascal, 77455 Marne-La-Vallée cedex 2, France.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 3, pp. 851-888

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The purpose of this work is to investigate the behavior of Multiscale Finite Element type methods for advection-diffusion problems in the advection-dominated regime. We present, study and compare various options to address the issue of the simultaneous presence of both heterogeneity of scales and strong advection. Classical MsFEM methods are compared with adjusted MsFEM methods, stabilized versions of the methods, and a splitting method that treats the multiscale diffusion and the strong advection separately.

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DOI : 10.1051/m2an/2016057
Classification : 35B27, 65M60, 65M12
Keywords: Homogenization, finite elements, highly oscillatory PDEs, advection-dominated problems

Le Bris, Claude 1 ; Legoll, Frédéric 1 ; Madiot, François 1

1 École des Ponts and INRIA, 6 et 8 avenue Blaise Pascal, 77455 Marne-La-Vallée cedex 2, France. 
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     title = {A numerical comparison of some {Multiscale} {Finite} {Element} approaches for advection-dominated problems in heterogeneous media},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
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Le Bris, Claude; Legoll, Frédéric; Madiot, François. A numerical comparison of some Multiscale Finite Element approaches for advection-dominated problems in heterogeneous media. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 3, pp. 851-888. doi: 10.1051/m2an/2016057

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