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An efficient symmetric finite volume element method for second-order variable coefficient parabolic integro-differential equations

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Abstract

This paper is devoted to develop a symmetric finite volume element (FVE) method to solve second-order variable coefficient parabolic integro-differential equations, arising in modeling of nonlocal reactive flows in porous media. Based on barycenter dual mesh, one semi-discrete and two fully discrete backward Euler and Crank–Nicolson symmetric FVE schemes are presented. Then, the optimal order error estimates in \(L^{2}\)-norm are derived for the semi-discrete and two fully discrete schemes. Numerical experiments are performed to examine the convergence rate and verify the effectiveness and usefulness of the new numerical schemes.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, People’s Republic of China

    Xiaoting Gan

  2. School of Mathematics and Statistics, Chuxiong Normal University, Chuxiong, 675000, People’s Republic of China

    Xiaoting Gan

  3. School of Automation, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Dengguo Xu

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  1. Xiaoting Gan
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  2. Dengguo Xu
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Correspondence to Xiaoting Gan.

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Communicated by Frederic Valentin.

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This work was supported by the National Natural Science Foundation of China (No. 61463002), the Science and Technology Program of Yunnan Province of China (2019FH001-079), and the Yunnan Provincial Department of Education Science Research Fund Project (No. 2019J0396).

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Gan, X., Xu, D. An efficient symmetric finite volume element method for second-order variable coefficient parabolic integro-differential equations. Comp. Appl. Math. 39, 264 (2020). https://doi.org/10.1007/s40314-020-01318-0

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  • DOI: https://doi.org/10.1007/s40314-020-01318-0

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