A three-field Multiscale Method
Numerical Analysis
2025-08-06 v2 Numerical Analysis
Abstract
\emph{A Three-Field Domain Decomposition Method} is the title of a seminal paper by F. Brezzi and L. D. Marini which introduces a three-field formulation for elliptic partial differential equations. Based on that, we propose the Multiscale-Hybrid-Hybrid Method (MHM) for the Darcy model, a multiscale finite element method that yields, after a series of formal manipulations, a symmetric positive definite formulation that depends only on the trace of the solution. We show stability and convergence results for a family of finite element spaces and establish relationships with other multiscale finite element methods.
Keywords
Cite
@article{arxiv.2404.16978,
title = {A three-field Multiscale Method},
author = {Franklin de Barros and Alexandre L. Madureira and Frédéric Valentin},
journal= {arXiv preprint arXiv:2404.16978},
year = {2025}
}