Mimetic Spectral Element Method for Anisotropic Diffusion

2018/02/13 by Marc Gerritsma, Artur Palha, Gerritsma, Marc +5 · 1 citation
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Soil, Finite Element Methods

paper · pdf · doi:10.48550/arxiv.1802.04597

openalex publication_date 2018/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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.

Citations

• Divergence free Virtual Elements for the Stokes problem on polygonal meshes

Cited by

• Explicit Time Mimetic Discretiztions Of Wave Equations

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