A numerical comparison of some Multiscale Finite Element approaches for advection-dominated problems in heterogeneous media
Received: 30 November 2015
Revised: 27 June 2016
Accepted: 30 August 2016
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.
Mathematics Subject Classification: 35B27 / 65M60 / 65M12
Key words: Homogenization / finite elements / highly oscillatory PDEs / advection-dominated problems
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