We design and analyze multigrid methods for the saddle point problems resulting from Raviart-Thomas-N\'ed\'elec mixed finite element methods (of order at least 1) for the Darcy system in porous media flow. Uniform convergence of the W-cycle algorithm in a nonstandard energy norm is established. Extensions to general second order elliptic problems are also addressed.
@article{arxiv.1511.08329,
title = {Multigrid Methods for Saddle Point Problems: Darcy Systems},
author = {Susanne C. Brenner and Duk-Soon Oh and Li-yeng Sung},
journal= {arXiv preprint arXiv:1511.08329},
year = {2015}
}