The stability of Ritz-Volterra projection and error estimates for finite element methods for a class of integro-differential equations of parabolic type

Yan Ping Lin; Tie Zhu Zhang

Applications of Mathematics (1991)

  • Volume: 36, Issue: 2, page 123-133
  • ISSN: 0862-7940

Abstract

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In this paper we first study the stability of Ritz-Volterra projection (see below) and its maximum norm estimates, and then we use these results to derive some error estimates for finite element methods for parabolic integro-differential equations.

How to cite

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Lin, Yan Ping, and Zhang, Tie Zhu. "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 36.2 (1991): 123-133. <http://eudml.org/doc/15664>.

@article{Lin1991,
abstract = {In this paper we first study the stability of Ritz-Volterra projection (see below) and its maximum norm estimates, and then we use these results to derive some $L^\infty $ error estimates for finite element methods for parabolic integro-differential equations.},
author = {Lin, Yan Ping, Zhang, Tie Zhu},
journal = {Applications of Mathematics},
keywords = {Ritz-Volterra projection; stability; finite element; error estimates; initial- boundary-value problem; parabolic Volterra integro-differential equation; stability; finite element methods; Ritz-Volterra projection; initial- boundary-value problem; parabolic Volterra integro-differential equation; error estimates},
language = {eng},
number = {2},
pages = {123-133},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The stability of Ritz-Volterra projection and error estimates for finite element methods for a class of integro-differential equations of parabolic type},
url = {http://eudml.org/doc/15664},
volume = {36},
year = {1991},
}

TY - JOUR
AU - Lin, Yan Ping
AU - Zhang, Tie Zhu
TI - The stability of Ritz-Volterra projection and error estimates for finite element methods for a class of integro-differential equations of parabolic type
JO - Applications of Mathematics
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 36
IS - 2
SP - 123
EP - 133
AB - In this paper we first study the stability of Ritz-Volterra projection (see below) and its maximum norm estimates, and then we use these results to derive some $L^\infty $ error estimates for finite element methods for parabolic integro-differential equations.
LA - eng
KW - Ritz-Volterra projection; stability; finite element; error estimates; initial- boundary-value problem; parabolic Volterra integro-differential equation; stability; finite element methods; Ritz-Volterra projection; initial- boundary-value problem; parabolic Volterra integro-differential equation; error estimates
UR - http://eudml.org/doc/15664
ER -

References

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  10. R. Rannacher R. Scott, Some optimal error estimates for piecewise linear finite element approximations, Math. Соmр. 38 (1982) 437-445. (1982) MR0645661
  11. A. H. Schatz V. Thomée L. Wahlbin, Maximum norm stability and error estimates in parabolic finite element equations, Comm. Pur. Appl. Math., XXXIII, (1980) 265-304. (1980) MR0562737
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  13. V. Thomee N. Y. Zhang, Error estimates for semi-discrete finite element methods for parabolic integro-differential equations, Math. Соmр., 53 (1989) 121-139. (1989) MR0969493
  14. M. F. Wheeler, 10.1137/0710062, SIAM J. Numer. Anal. 19 (1973) 723-759. (1973) MR0351124DOI10.1137/0710062

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