A Finite Element Framework for Some Mimetic Finite Difference\n Discretizations

2015/03/15 by Carmen Rodrigo, Francisco J. Gaspar, Rodrigo, Carmen +5
Engineering · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Lattice Boltzmann Simulation Studies #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1503.04423

openalex publication_date 2015/03/15 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In this work we derive equivalence relations between mimetic finite\ndifference schemes on simplicial grids and modified N 'ed 'elec-Raviart-Thomas\nfinite element methods for model problems in\n\H( curl) and H(÷). This\nprovides a simple and transparent way to analyze such mimetic finite difference\ndiscretizations using the well-known results from finite element theory. The\nfinite element framework that we develop is also crucial for the design of\nefficient multigrid methods for mimetic finite difference discretizations,\nsince it allows us to use canonical inter-grid transfer operators arising from\nthe finite element framework. We provide special Local Fourier Analysis and\nnumerical results to demonstrate the efficiency of such multigrid methods.\n

Related

• Simple finite element schemes for the solution of the curl-div system
• On low order mimetic finite difference methods
• Connections Between Finite Difference and Finite Element Approximations
• Numerical results for mimetic discretization of Reissner-Mindlin plate problems
• Convergence analysis of the mimetic finite difference method for elliptic problems with staggered discretization of the diffusion coefficients