A finite element framework for some mimetic finite difference discretizations

A finite element framework for some mimetic finite difference discretizations

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Article ID: iaor201530415
Volume: 70
Issue: 11
Start Page Number: 2661
End Page Number: 2673
Publication Date: Dec 2015
Journal: Computers and Mathematics with Applications
Authors: , , ,
Keywords: engineering
Abstract:

In this work we derive equivalence relations between mimetic finite difference schemes on simplicial grids and modified Nédélec–Raviart–Thomas finite element methods for model problems in H ( curl ) equ1 and H ( div ) equ2. This provides a simple and transparent way to analyze such mimetic finite difference discretizations using the well‐known results from finite element theory. The finite element framework that we develop is also crucial for the design of efficient multigrid methods for mimetic finite difference discretizations, since it allows us to use canonical inter‐grid transfer operators arising from the finite element framework. We provide special Local Fourier Analysis and numerical results to demonstrate the efficiency of such multigrid methods.

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