A Three-Field Multiscale Method
<|reference_start|>A Three-Field Multiscale Method: "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 (MH$^2$M) 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.<|reference_end|>
@article{de barros2024a,
    title={A Three-Field Multiscale Method},
    author={Franklin de Barros, Alexandre L. Madureira, Fr'ed'eric Valentin},
    journal={arXiv preprint arXiv:2404.16978},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.16978},
    primaryClass={math.NA cs.NA}
}