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Asymptotic expansions and Richardson extrapolation of approximate solutions for integro-differential equations by mixed finite element methods

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Abstract

In this paper asymptotic error expansions for mixed finite element approximations of the integro-differential equation are derived, and Richardson extrapolation is applied to improve the accuracy of the approximations by two different schemes with the help of an interpolation post-processing technique. The results of this paper provide new asymptotic expansions. As a by-product, we illustrate that all the approximations of higher accuracy can be used to form a class of a-posteriori error estimators for this mixed finite element method. Finally, a numerical example is provided to validate the theoretical results.

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Authors and Affiliations

  1. School of Applied Mathematics, Central University of Finance and Economics, Beijing, 100081, China

    Shanghui Jia

  2. Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, P7B 5E1, Canada

    Deli Li

  3. Department of Mathematics, Tianjin University of Finance and Economics, Tianjin, 300222, China

    Shuhua Zhang

  4. Liu Hui Center for Applied Mathematics, Nankai University, Tianjin, 300071, China

    Shuhua Zhang

  5. Tianjin University, Tianjin, 300072, China

    Shuhua Zhang

Authors
  1. Shanghui Jia
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  2. Deli Li
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  3. Shuhua Zhang
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Corresponding author

Correspondence to Shanghui Jia.

Additional information

Communicated by Yuesheng Xu.

This project was supported in part by the Special Funds for Major State Basic Research Project (2007CB8149), the National Natural Science Foundation of China (10471103 and 10771158), Social Science Foundation of the Ministry of Education of China (Numerical Methods for Convertible Bonds, 06JA630047), the NSERC, Tianjin Natural Science Foundation (07JCYBJC14300), Tianjin Educational Committee, Liu Hui Center for Applied Mathematics of Nankai University and Tianjin University, and Tianjin University of Finance and Economics.

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Jia, S., Li, D. & Zhang, S. Asymptotic expansions and Richardson extrapolation of approximate solutions for integro-differential equations by mixed finite element methods. Adv Comput Math 29, 337–356 (2008). https://doi.org/10.1007/s10444-007-9052-5

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  • DOI: https://doi.org/10.1007/s10444-007-9052-5

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