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Weak Galerkin finite element method for the parabolic integro-differential equation with weakly singular kernel

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Abstract

A weak Galerkin finite element/backward Euler scheme for the parabolic integro-differential equation with weakly singular kernel is considered. The stability and optimal convergence order estimate of the weak Galerkin finite element scheme in \(L^2\) norm are derived. Numerical experiment verifies our theory finding.

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Acknowledgements

This work was supported by the National Science Foundation of China (contract Grant number 11671131) and Scientific Research Fund of Hunan Provincial Education Department (No. 15A110).

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Authors and Affiliations

  1. Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), College of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China

    Jun Zhou, Da Xu & Xiuxiu Dai

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  1. Jun Zhou
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  2. Da Xu
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  3. Xiuxiu Dai
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Correspondence to Da Xu.

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Communicated by Abimael Loula.

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Zhou, J., Xu, D. & Dai, X. Weak Galerkin finite element method for the parabolic integro-differential equation with weakly singular kernel. Comp. Appl. Math. 38, 38 (2019). https://doi.org/10.1007/s40314-019-0807-7

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