Colloquium: Optimal error estimate for multiscale finite element method with periodic media

Colloquium| Institute of Mathematical Sciences

Abstract: We derive the optimal energy error estimate for multiscale finite element method (MsFEM) with oversampling technique applying to elliptic systems with rapidly oscillating periodic coefficients, which are assumed to be bounded and measurable. Such media admits rough microstructures. As a by-product of the energy estimate, we derive the rate of convergence in L$^{d/(d-1)}$ norm. We shall also discuss tthe extension of the present results to more general media such as the locally periodic media. This is a joint work with Siqi Song.