Non-intrusive coupling: multiscale computation and finite element mesh adaptation

In this paper, we present an iterative coupling algorithm for solving multiscale problems, in a non-intrusive way (cf. [4, 5]). Let us consider a global linear finite element model on Ω = ΩG ∪ ΩG̃, and a local (potentially non-linear) model on ΩL (cf. Fig. 1). The purpose of such algorithm is to replace the linear model on the area of interest ΩG̃ by the local model ΩL, without altering the numerical operator associated with the initial global model on Ω (for example the stiffness matrix K).