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New locally conservative finite element methods on a rectangular mesh

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Abstract

A new family of locally conservative, finite element methods for a rectangular mesh is introduced to solve second-order elliptic equations. Our approach is composed of generating PDE-adapted local basis and solving a global matrix system arising from a flux continuity equation. Quadratic and cubic elements are analyzed and optimal order error estimates measured in the energy norm are provided for elliptic equations. Next, this approach is exploited to approximate Stokes equations. Numerical results are presented for various examples including the lid driven-cavity problem.

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Acknowledgments

The authors would like to express sincere thanks to anonymous referees whose invaluable comments led to an improved version of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Ajou University, Suwon, 443-749, Korea

    Youngmok Jeon

  2. Department of Computational Science and Engineering, Yonsei University, Seoul, 120-749, Korea

    Eun-Jae Park

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  1. Youngmok Jeon
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  2. Eun-Jae Park
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Corresponding author

Correspondence to Youngmok Jeon.

Additional information

Research of Y. Jeon was supported by NRF 2010-0021683, and E.-J. Park was supported in part by the WCU program through NRF R31-10049.

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Jeon, Y., Park, EJ. New locally conservative finite element methods on a rectangular mesh. Numer. Math. 123, 97–119 (2013). https://doi.org/10.1007/s00211-012-0477-5

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  • DOI: https://doi.org/10.1007/s00211-012-0477-5

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