| Title:
|
The stability of Ritz-Volterra projection and error estimates for finite element methods for a class of integro-differential equations of parabolic type (English) |
| Author:
|
Lin, Yanping |
| Author:
|
Zhang, Tie |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
36 |
| Issue:
|
2 |
| Year:
|
1991 |
| Pages:
|
123-133 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Ritz-Volterra projection |
| Keyword:
|
stability |
| Keyword:
|
finite element |
| Keyword:
|
error estimates |
| Keyword:
|
initial- boundary-value problem |
| Keyword:
|
parabolic Volterra integro-differential equation |
| MSC:
|
45K05 |
| MSC:
|
65M60 |
| MSC:
|
65N30 |
| MSC:
|
65R20 |
| idZBL:
|
Zbl 0732.65122 |
| idMR:
|
MR1097696 |
| DOI:
|
10.21136/AM.1991.104449 |
| . |
| Date available:
|
2008-05-20T18:41:11Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104449 |
| . |
| Reference:
|
[1] J. R. Cannon, Yanping Lin: Non-classical $H^1$ projection and Galerkin methods for nonlinear parabolic integro-differential equations.Calcolo, 25 (1988) 187- 201, MR 1053754, 10.1007/BF02575943 |
| Reference:
|
[2] J. R. Cannon Y. Lin: A priori $L^2$ error estimates for finite element methods for nonlinear diffusion equations with memory.SJAM. J. Numer. Anal., 27 (1990) 595-607. MR 1041253, 10.1137/0727036 |
| Reference:
|
[3] P. G. Ciarlet: The Finite Element Method for Elliptic Problems.North Holland, 1978. Zbl 0383.65058, MR 0520174 |
| Reference:
|
[4] E. Green-Yanik G. Fairweather: Finite element methods for parabolic and hyperbolic partial integro-differential equations.to appear in Nonlinear Analysis. MR 0954953 |
| Reference:
|
[5] M. N. Le Roux V. Thomee: Numerical solution of semilinear integro-differential equations of parabolic type.SIAM J. Numer. Anal., 26 (1989) 1291-1309. MR 1025089, 10.1137/0726075 |
| Reference:
|
[6] Y. Lin V. Thomee L. Wahlbin: A Ritz-Volterra projection onto finite element spaces and application to integro and related equations.to appear in SIAM J. Numer. Anal. MR 1111453 |
| Reference:
|
[7] Qun Lin, Tao Lu, Shu-min Shen: Maximum norm estimate, extrapolation and optimal points of stresses for the finite element methods on the strongly regular triangulalion.J. Соmр. Math., Vol. 1, No. 4 (1983) 376-383. MR 0726394 |
| Reference:
|
[8] Qun Lin, Qi-ding Zhou: Superconvergence Theory of Finite Element Methods.Book to appear. |
| Reference:
|
[9] J. A. Nitsche: $L_{\infty}$-convergence of finite element Galerkin approximations for parabolic problems.R.A.I.R.O., Vol. 13, No. 1, (1979) 31-51. Zbl 0401.65069, MR 0527037 |
| Reference:
|
[10] R. Rannacher R. Scott: Some optimal error estimates for piecewise linear finite element approximations.Math. Соmр. 38 (1982) 437-445. MR 0645661 |
| Reference:
|
[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. MR 0562737 |
| Reference:
|
[12] R. Scott: Optimal $L^{\infty}$ estimates for the finite element on irregular meshes.Math. Соmр., 30 (1976) 681-697. Zbl 0349.65060, MR 0436617 |
| Reference:
|
[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. MR 0969493 |
| Reference:
|
[14] M. F. Wheeler: A priori $L_2$ error estimates for Galerkin methods to parabolic partial differential equations.SIAM J. Numer. Anal. 19 (1973) 723-759. MR 0351124, 10.1137/0710062 |
| . |
