An immediate analysis for global superconvergence for integrodifferential equations

Qun Lin; Shu Hua Zhang

Applications of Mathematics (1997)

  • Volume: 42, Issue: 1, page 1-21
  • ISSN: 0862-7940

Abstract

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In this paper we study the finite element approximations to the parabolic and hyperbolic integrodifferential equations and present an immediate analysis for global superconvergence for these problems, without using the Ritz projection or its modified forms.

How to cite

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Lin, Qun, and Zhang, Shu Hua. "An immediate analysis for global superconvergence for integrodifferential equations." Applications of Mathematics 42.1 (1997): 1-21. <http://eudml.org/doc/32964>.

@article{Lin1997,
abstract = {In this paper we study the finite element approximations to the parabolic and hyperbolic integrodifferential equations and present an immediate analysis for global superconvergence for these problems, without using the Ritz projection or its modified forms.},
author = {Lin, Qun, Zhang, Shu Hua},
journal = {Applications of Mathematics},
keywords = {integrodifferential equations; global superconvergence; immediate analysis; postprocessing; finite element method; parabolic; hyperbolic; global superconvergence; integro-differential equations; postprocessing; finite element method; parabolic; hyperbolic},
language = {eng},
number = {1},
pages = {1-21},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An immediate analysis for global superconvergence for integrodifferential equations},
url = {http://eudml.org/doc/32964},
volume = {42},
year = {1997},
}

TY - JOUR
AU - Lin, Qun
AU - Zhang, Shu Hua
TI - An immediate analysis for global superconvergence for integrodifferential equations
JO - Applications of Mathematics
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 42
IS - 1
SP - 1
EP - 21
AB - In this paper we study the finite element approximations to the parabolic and hyperbolic integrodifferential equations and present an immediate analysis for global superconvergence for these problems, without using the Ritz projection or its modified forms.
LA - eng
KW - integrodifferential equations; global superconvergence; immediate analysis; postprocessing; finite element method; parabolic; hyperbolic; global superconvergence; integro-differential equations; postprocessing; finite element method; parabolic; hyperbolic
UR - http://eudml.org/doc/32964
ER -

References

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  3. A new observation in FEM, Proc. Syst. Sci. & Syst. Eng., Great Wall (H.K.), Culture Publish Co., 1991, pp. 389–391. (1991) 
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  6. 10.1137/0727037, SIAM J. Numer. Anal. 27 (1990), 608–621. (1990) Zbl0703.65095MR1041254DOI10.1137/0727037
  7. The stability of Ritz-Volterra projection and error estimates for finite element methods for a class of integro-differential equations of parabolic type, Applications of Mathematics 36 (1991), no. 2, 123–133. (1991) MR1097696
  8. 10.1137/0728056, SIAM J. Numer. Anal. 28 (1991), 1047–1070. (1991) MR1111453DOI10.1137/0728056
  9. Galerkin Finite Element Methods for Parabolic Problems, Lect. Notes in Math., 1054, 1984. (1984) MR0744045
  10. 10.1137/0726033, SIAM J. Numer. Anal. 26 (1989), 553–573. (1989) MR0997656DOI10.1137/0726033
  11. 10.2307/2008352, Math. Comp. 53 (1989), 121–139. (1989) MR0969493DOI10.2307/2008352
  12. 10.1137/0710062, SIAM J. Numer. Anal. 10 (1973), 723–759. (1973) MR0351124DOI10.1137/0710062
  13. Superconvergence Theory of the Finite Element Methods, Hunan Science Press, 1990. (1990) 

Citations in EuDML Documents

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  1. Shu Hua Zhang, Yan Ping Lin, Ming Rao, Numerical solutions for second-kind Volterra integral equations by Galerkin methods
  2. Shu Hua Zhang, Tao Lin, Yan Ping Lin, Ming Rao, Defect correction and a posteriori error estimation of Petrov-Galerkin methods for nonlinear Volterra integro-differential equations
  3. Qun Lin, Tang Liu, Shu Hua Zhang, Superconvergence estimates of finite element methods for American options
  4. Qun Lin, Shu Hua Zhang, A direct global superconvergence analysis for Sobolev and viscoelasticity type equations
  5. Shanghui Jia, Deli Li, Tang Liu, Shu Hua Zhang, Richardson extrapolation and defect correction of mixed finite element methods for integro-differential equations in porous media

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