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A finite element framework for some mimetic finite difference discretizations

Authors:

L. ZikatanovAuthors Info & Claims

Computers & Mathematics with Applications, Volume 70, Issue 11

Pages 2661 - 2673

https://doi.org/10.1016/j.camwa.2015.07.012

Published: 01 December 2015 Publication History

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.

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Cited By

Ahmed ENordbotten JRadu F(2020)Adaptive asynchronous time-stepping, stopping criteria, and a posteriori error estimates for fixed-stress iterative schemes for coupled poromechanics problemsJournal of Computational and Applied Mathematics10.1016/j.cam.2019.06.028364:COnline publication date: 15-Jan-2020
https://dl.acm.org/doi/10.1016/j.cam.2019.06.028

A finite element framework for some mimetic finite difference discretizations
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
2. Theory of computation

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cover image Computers & Mathematics with Applications

Computers & Mathematics with Applications Volume 70, Issue 11

December 2015

167 pages

ISSN:0898-1221

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Copyright © Elsevier Ltd.

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Pergamon Press, Inc.

United States

Publication History

Published: 01 December 2015

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Cited By

Ahmed ENordbotten JRadu F(2020)Adaptive asynchronous time-stepping, stopping criteria, and a posteriori error estimates for fixed-stress iterative schemes for coupled poromechanics problemsJournal of Computational and Applied Mathematics10.1016/j.cam.2019.06.028364:COnline publication date: 15-Jan-2020
https://dl.acm.org/doi/10.1016/j.cam.2019.06.028

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