Superconvergence and gradient recovery for a finite volume element method for solving convection-diffusion equations

Authors

  • Tie Zhang,

    Corresponding author
    1. Department of Mathematics and State Key Laboratory of SAPI Technology and Research Center of National Metallurgical Automation, Northeastern University, Shenyang, China
    • Correspondence to: Tie Zhang, Department of Mathematics, Northeastern University, Shenyang, 110004, China, (e-mail: ztmath@163.com)

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  • Ying Sheng

    1. Department of Mathematics and State Key Laboratory of SAPI Technology and Research Center of National Metallurgical Automation, Northeastern University, Shenyang, China
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Abstract

We study the superconvergence of the finite volume element (FVE) method for solving convection-diffusion equations using bilinear trial functions. We first establish a superclose weak estimate for the bilinear form of FVE method. Based on this estimate, we obtain the H1-superconvergence result: math formula. Then, we present a gradient recovery formula and prove that the recovery gradient possesses the math formula-order superconvergence. Moreover, an asymptotically exact a posteriori error estimate is also given for the gradient error of FVE solution.Copyright © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1152–1168, 2014

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