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Finite volume element method with Lagrangian cubic functions

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Abstract

This paper establishes a new finite volume element scheme for Poisson equation on triangular meshes. The trial function space is taken as Lagrangian cubic finite element space on triangular partition, and the test function space is defined as piecewise constant space on dual partition. Under some weak condition about the triangular meshes, the authors prove that the stiffness matrix is uniformly positive definite and convergence rate to be O(h 3) in H 1-norm. Some numerical experiments confirm the theoretical considerations.

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Authors and Affiliations

  1. Institute of Mathematics, Jilin University, Changchun, 130012, China

    Yuqiong Ding & Yonghai Li

Authors
  1. Yuqiong Ding
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  2. Yonghai Li
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Correspondence to Yuqiong Ding.

Additional information

This research is supported by the ‘985’ programme of Jilin University, the National Natural Science Foundation of China under Grant Nos. 10971082 and 11076014.

This paper was recommended for publication by Editor Ningning YAN.

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Ding, Y., Li, Y. Finite volume element method with Lagrangian cubic functions. J Syst Sci Complex 24, 991–1006 (2011). https://doi.org/10.1007/s11424-011-9113-1

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  • DOI: https://doi.org/10.1007/s11424-011-9113-1

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