A Nitsche Hybrid Multiscale Method with Non-matching Grids

We propose a Nitsche method for multiscale partial differential equations, which retrieves the macroscopic information and the local microscopic information at one stroke. We prove the convergence of the method for second order elliptic problem with bounded and measurable coefficients. The rate of convergence may be derived for coefficients with further structures such as periodicity and ergodicity. Extensive numerical results confirm the theoretical predictions.

Automated summary

This article proposes a Nitsche method for multiscale partial differential equations, which is able to retrieve both macroscopic and microscopic information simultaneously. It proves the convergence of the method for second order elliptic problems with bounded and measurable coefficients, and also derives the convergence rate for coefficients with further structures like periodicity and ergodicity. Extensive numerical results confirm the theoretical predictions.