Mimetic Spectral Element Method for Anisotropic Diffusion
Provides a stable, high-order numerical method for anisotropic diffusion problems, which is important for computational physics and engineering applications.
The paper develops a mimetic spectral element method for anisotropic diffusion that achieves point-wise divergence-free solutions and optimal convergence on orthogonal and non-affine grids.
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.