A numerical comparison of some Multiscale Finite Element approaches for convection-dominated problems in heterogeneous media
For researchers in computational geoscience or engineering dealing with multiscale transport problems, this is an incremental comparison of existing methods.
This work compares Multiscale Finite Element methods for advection-diffusion problems in heterogeneous media under advection-dominated regimes, finding that adjusted and stabilized methods outperform classical approaches, though no specific numerical gains are reported.
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.