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Linear Systems Arising for Second-Order Mimetic Divergence and Gradient Discretizations

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Journal of Mathematical Modelling and Algorithms

Abstract

Recent investigations by Castillo and Grone have led to a new method for constructing mimetic discretizations of divergence and gradient operators. Their technique, which employs a matrix formulation to incorporate mimetic constraints, is capable of producing approximations whose order at a grid boundary is equal to that in the grid’s interior. In this paper, we construct a second-order mimetic discretization using Castillo and Grone’s approach and compare it to other second-order discretizations by applying them to an elliptic boundary value problem in one dimension. A detailed perturbation analysis is provided to offer some insight into the two discretizations yielding the best numerical results in the study.

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References

  1. Castillo, J. E. and Grone, R.: A matrix analysis to higher-order approximations for divergence and gradients satsifying a global conservation law, SIAM J. Matrix Anal. Appl. 25 (2003), 128–142.

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Author information

Authors and Affiliations

  1. Computational Science Research Center, San Diego State University, San Diego, CA, 92182-1245, USA

    Jose E. Castillo

  2. Raytheon Company, 8680 Balboa Avenue, San Diego, CA, 92123, USA

    Mark Yasuda

Authors
  1. Jose E. Castillo
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  2. Mark Yasuda
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Corresponding author

Correspondence to Jose E. Castillo.

Additional information

Mathematics Subject Classifications (2000)

65D25, 65M06, 65G99.

This paper is an expanded version of the article [2] presented at the International Conference on Parallel and Distributed Processing Techniques and Applications held in Las Vegas, Nevada in June of 2003.

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Castillo, J.E., Yasuda, M. Linear Systems Arising for Second-Order Mimetic Divergence and Gradient Discretizations. J Math Model Algor 4, 67–82 (2005). https://doi.org/10.1007/s10852-004-3523-1

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  • DOI: https://doi.org/10.1007/s10852-004-3523-1

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