Mimetic Spectral Element Method for Anisotropic Diffusion

Abstract

This chapter addresses the topological structure of steady, anisotropic, inhomogeneous diffusion problems. Differential operators are represented by sparse incidence matrices, while weighted mass matrices play the role of metric-dependent Hodge matrices. The resulting mixed formulation is point-wise divergence-free if the right hand side function f = 0. The method is inf-sup stable; no stabilization is required and the method displays optimal convergence on orthogonal and deformed grids.