NON-CONFORMING MULTISCALE FINITE ELEMENT METHOD FOR STOKES FLOWS IN HETEROGENEOUS MEDIA. PART II: ERROR ESTIMATES FOR PERIODIC MICROSTRUCTURE

This paper is dedicated to the rigorous numerical analysis of a Mul-tiscale Finite Element Method (MsFEM) for the Stokes system, when dealing with highly heterogeneous media, as proposed in B.P. Muljadi et al., Non-conforming multiscale finite Element method for Stokes flows in heterogeneous media. Part I: Methodologies and numerical experiments, SIAM MMS (2015), 13(4) 1146--1172. The method is in the vein of the classical Crouzeix-Raviart approach. It is generalized here to arbitrary sets of weighting functions used to enforce continuity across the mesh edges. We provide error bounds for a particular set of weighting functions in a periodic setting, using an accurate estimate of the homogenization error. Numerical experiments demonstrate an improved accuracy of the present variant with respect to that of Part I, both in the periodic case and in a broader setting.

Automated summary

This paper presents a rigorous numerical analysis of a Multiscale Finite Element Method (MsFEM) for the Stokes system in highly heterogeneous media, based on the approach proposed by B.P. Muljadi et al. The method extends the classical Crouzeix-Raviart approach by generalizing it to arbitrary sets of weighting functions for enforcing continuity across mesh edges. Error bounds are provided for a specific set of weighting functions in a periodic setting, using an accurate estimate of the homogenization error. Numerical experiments demonstrate improved accuracy compared to Part I, both in the periodic case and in a broader setting.