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L 2 error estimates and superconvergence of the finite volume element methods on quadrilateral meshes

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Abstract

This paper is concerned with the finite volume element methods on quadrilateral mesh for second-order elliptic equation with variable coefficients. An error estimate in L 2 norm is shown on the quadrilateral meshes consisting of h 2-parallelograms. Superconvergence of numerical solution is also derived in an average gradient norm on h 2-uniform quadrilateral meshes. Numerical examples confirm our theoretical conclusions.

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Authors and Affiliations

  1. School of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China

    Junliang Lv & Yonghai Li

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  1. Junliang Lv
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  2. Yonghai Li
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Correspondence to Yonghai Li.

Additional information

Communicated by Z. Chen.

Supported by the ‘985’ program of Jilin University, the Basic Research Foundation of Jilin University, the Young Fund of School of Mathematics at Jilin University, National Natural Science Foundation of China (no. 10971082), and the NSAF of China (no. 11076014).

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Lv, J., Li, Y. L 2 error estimates and superconvergence of the finite volume element methods on quadrilateral meshes. Adv Comput Math 37, 393–416 (2012). https://doi.org/10.1007/s10444-011-9215-2

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  • DOI: https://doi.org/10.1007/s10444-011-9215-2

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