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A Mixed Finite-Element Method on Polytopal Mesh

Abstract

In this paper, we introduce new stable mixed finite elements of any order on polytopal mesh for solving second-order elliptic problem. We establish optimal order error estimates for velocity and super convergence for pressure. Numerical experiments are conducted for our mixed elements of different orders on 2D and 3D spaces that confirm the theory.

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Acknowledgements

This research was supported in part by the National Science Foundation Grant DMS-1620016. This work was also supported in parts by HKSAR grant Q81Q and JRI of The Hong Kong Polytechnic University.

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Correspondence to Shangyou Zhang.

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On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Lin, Y., Ye, X. & Zhang, S. A Mixed Finite-Element Method on Polytopal Mesh. Commun. Appl. Math. Comput. 4, 1374–1385 (2022). https://doi.org/10.1007/s42967-021-00180-z

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  • DOI: https://doi.org/10.1007/s42967-021-00180-z

Keywords

  • Mixed finite-element methods
  • Second-order elliptic problem
  • Polytopal mesh

Mathematics Subject Classification

  • 65N15
  • 65N30
  • 35B45
  • 35J50