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A Nonconforming Characteristic Finite Element Method for Nonlinear Advection-Dominated Diffusion Equation with Memory Term

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Book cover Proceedings of The Eighth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA), 2013

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 212))

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Abstract

A nonconforming characteristic finite element method is considered for nonlinear convection-dominated diffusion equation with memory term. By the use of some special properties of the finite element interpolation operator, and without Rietz-Volterra projection operator which is an indispensable tool in the convergence analysis of finite element methods for integro-differential evolution equations in the previous literature, the optimal error estimate on L 2-norm and the superconvergence result on H 1-norm are obtained.

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Acknowledgments

This research is supported by National Natural Science Foundation of China (No. 60876014), the Natural Science Foundation of the Education Department of Henan Province (No. 2010B110017), and the Natural Science Foundation of LuoYang Institute of Science and Technology (No. 2011YZ1106).

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Authors and Affiliations

  1. Department of Mathematics and Physics, Luoyang Institute of Science and Technology, Luoyang, 471023, People’s Republic of China

    Jiaquan Zhou, Chao Xu & Jianlai Gao

Authors
  1. Jiaquan Zhou
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  2. Chao Xu
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  3. Jianlai Gao
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Corresponding author

Correspondence to Jiaquan Zhou .

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Editors and Affiliations

  1. School of Science, Anhui University of Science & Technology, Huainan, China

    Zhixiang Yin

  2. Huazhong University of Science and Technology, Wuhan, China

    Linqiang Pan

  3. Anhui University of Science & Technology, Huainan, China

    Xianwen Fang

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Zhou, J., Xu, C., Gao, J. (2013). A Nonconforming Characteristic Finite Element Method for Nonlinear Advection-Dominated Diffusion Equation with Memory Term. In: Yin, Z., Pan, L., Fang, X. (eds) Proceedings of The Eighth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA), 2013. Advances in Intelligent Systems and Computing, vol 212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37502-6_22

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  • DOI: https://doi.org/10.1007/978-3-642-37502-6_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37501-9

  • Online ISBN: 978-3-642-37502-6

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