A Nitsche Hybrid multiscale method with non-matching grids

TL;DR

This paper introduces a Nitsche hybrid multiscale method capable of efficiently capturing both macro and micro-scale information in PDEs, with proven convergence and validated by numerical experiments.

Contribution

It presents a novel Nitsche-based multiscale method that simultaneously retrieves macro and micro-scale data for elliptic PDEs, with theoretical convergence analysis.

Findings

Method converges for second order elliptic problems

Convergence rate established for structured coefficients

Numerical results confirm theoretical predictions

Abstract

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.