A finite element framework for some mimetic finite difference discretizations

C. Rodrigo, F. J. Gaspar, X. Hu, L. Zikatanov

Research output: Contribution to journalArticle

2 Citations (Scopus)

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) and H(div). 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.

Original languageEnglish (US)
Pages (from-to)2661-2673
Number of pages13
JournalComputers and Mathematics with Applications
Volume70
Issue number11
DOIs
StatePublished - Dec 2015

Fingerprint

Fourier analysis
Finite Difference
Discretization
Multigrid Method
Finite Element
Finite element method
Grid
Transfer Operator
Curl
Fourier Analysis
Equivalence relation
Finite Difference Scheme
Finite Element Method
Numerical Results
Demonstrate
Framework
Model

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

Cite this

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A finite element framework for some mimetic finite difference discretizations. / Rodrigo, C.; Gaspar, F. J.; Hu, X.; Zikatanov, L.

In: Computers and Mathematics with Applications, Vol. 70, No. 11, 12.2015, p. 2661-2673.

Research output: Contribution to journalArticle

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