This paper addresses the topological structure of steady, anisotropic, inhomogeneous diffusion problems. Two discrete formulations: a) mixed and b) direct formulations are discussed. Differential operators are represented by sparse incidence matrices, while weighted mass matrices play the role of metric-dependent Hodge matrices. The resulting mixed formulations are point-wise divergence-free if the right hand side function f = 0. The method is inf-sup stable and displays optimal convergence on orthogonal and non-affine grids.
@article{arxiv.1802.04597,
title = {Mimetic Spectral Element Method for Anisotropic Diffusion},
author = {Marc Gerritsma and Artur Palha and Varun Jain and Yi Zhang},
journal= {arXiv preprint arXiv:1802.04597},
year = {2018}
}