| Title:
|
A direct global superconvergence analysis for Sobolev and viscoelasticity type equations (English) |
| Author:
|
Lin, Qun |
| Author:
|
Zhang, Shuhua |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
42 |
| Issue:
|
1 |
| Year:
|
1997 |
| Pages:
|
23-34 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we study the finite element approximations to the Sobolev and viscoelasticity type equations and present a direct analysis for global superconvergence for these problems, without using Ritz projection or its modified forms. (English) |
| Keyword:
|
Sobolev and viscoelasticity type equations |
| Keyword:
|
global superconvergence |
| Keyword:
|
direct analysis |
| Keyword:
|
finite element method |
| Keyword:
|
evolution equation |
| MSC:
|
35G10 |
| MSC:
|
35K25 |
| MSC:
|
65B05 |
| MSC:
|
65M12 |
| MSC:
|
65M60 |
| MSC:
|
65N30 |
| MSC:
|
74Hxx |
| idZBL:
|
Zbl 0902.65034 |
| idMR:
|
MR1426678 |
| DOI:
|
10.1023/A:1022288409629 |
| . |
| Date available:
|
2009-09-22T17:53:18Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134342 |
| . |
| Reference:
|
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| Reference:
|
[2] R. Ewing: The approximation of certain parabolic equations backward in time by Sobolev equations.SIAM J. Math. Anal. 6 (1975), 283–294. Zbl 0292.35004, MR 0361447, 10.1137/0506029 |
| Reference:
|
[3] R. Ewing: Numerical solution of Sobolev partial differential eqautions.SIAM J. Numer. Anal. 12 (1975), 345–363. MR 0395265, 10.1137/0712028 |
| Reference:
|
[4] W. Ford: Galerkin approximation to nonlinear pseudoparabolic partial differential equation.Aequationes Math. 14 (1976), 271–291. MR 0408270, 10.1007/BF01835978 |
| Reference:
|
[5] W. Ford, T. Ting: Stability and convergence of difference approximations to pseudoparabolic partial equations.Math. Comp. 27 (1973), 737–743. MR 0366052, 10.1090/S0025-5718-1973-0366052-4 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Q. Lin, N. Yan, A. Zhou: A rectangle test for interpolated finite elements, ibid.217–229. |
| Reference:
|
[9] Q. Lin, S. Zhang: An immediate analysis for global superconvergence for integrodifferential equations.Appl. Math. 42 (1997), 1–21. MR 1426677, 10.1023/A:1022264125558 |
| Reference:
|
[10] Y. Lin: Galerkin methods for nonlinear Sobolev equations.Aequations Math. 40 (1990), 54–56. Zbl 0734.65078, MR 1055190, 10.1007/BF02112280 |
| Reference:
|
[11] Y. Lin, T. Zhang: Finite element methods for nonlinear Sobolev equations with nonlinear boundary conditions.J. Math. Anal. & Appl. 165 (1992), 180–191. MR 1151067, 10.1016/0022-247X(92)90074-N |
| Reference:
|
[12] Y. Lin, V. Thomée, L. Wahlbin: Ritz-Volterra projection on finite element spaces and applications to integrodifferential and related equations.SIAM J. Numer. Anal. 28 (1991), 1047–1070. MR 1111453, 10.1137/0728056 |
| Reference:
|
[13] M. Nakao: Error estimates of a Galerkin method for some nonlinear Sobolev equations in one space dimension.Numer. Math. 47 (1985), 139–157. Zbl 0575.65112, MR 0797883, 10.1007/BF01389881 |
| Reference:
|
[14] L. Wahlbin: Error estimates for a Galerkin method for a class of model equations for long waves.Numer. Math. 23 (1975), 289–303. Zbl 0283.65052, MR 0388799, 10.1007/BF01438256 |
| Reference:
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[15] M. Wheeler: A priori $L_2$ error estimates for Galerkin approximations to parabolic partial differential equations.SIAM J. Numer. Anal. 10 (1973), 723–759. MR 0351124, 10.1137/0710062 |
| Reference:
|
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| . |
