Article
MSC:
35G10,
35K25,
65B05,
65M12,
65M60,
65N30,
74Hxx | MR 1426678 | Zbl 0902.65034 | DOI: 10.1023/A:1022288409629
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Keywords:
Sobolev and viscoelasticity type equations; global superconvergence; direct analysis; finite element method; evolution equation
Sobolev and viscoelasticity type equations; global superconvergence; direct analysis; finite element method; evolution equation
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.
References:
[1] D. Arnold, J. Douglas, V. Thomée: Superconvergence of a finite element approximation to the solution of a Sobolev equation in a single space variable. Math. Comp. 36 (1981), 53–63. DOI 10.1090/S0025-5718-1981-0595041-4 | MR 0595041
[2] R. Ewing: The approximation of certain parabolic equations backward in time by Sobolev equations. SIAM J. Math. Anal. 6 (1975), 283–294. DOI 10.1137/0506029 | MR 0361447 | Zbl 0292.35004
[3] R. Ewing: Numerical solution of Sobolev partial differential eqautions. SIAM J. Numer. Anal. 12 (1975), 345–363. DOI 10.1137/0712028 | MR 0395265
[4] W. Ford: Galerkin approximation to nonlinear pseudoparabolic partial differential equation. Aequationes Math. 14 (1976), 271–291. DOI 10.1007/BF01835978 | MR 0408270
[5] W. Ford, T. Ting: Stability and convergence of difference approximations to pseudoparabolic partial equations. Math. Comp. 27 (1973), 737–743. DOI 10.1090/S0025-5718-1973-0366052-4 | MR 0366052
[6] W. Ford, T. Ting: Uniform error estimates for difference approximations to nonlinear pseudoparabolic partial differential equations. SIAM J. Numer. Anal. 11 (1974), 155–169. DOI 10.1137/0711016 | MR 0423833
[7] Q. Lin: A new observation in FEM. Proc. Syst. Sci. & Syst. Eng. (1991), Great Wall (H.K.) Culture Publish Co., 389–391.
[8] Q. Lin, N. Yan, A. Zhou: A rectangle test for interpolated finite elements, ibid. 217–229.
[9] Q. Lin, S. Zhang: An immediate analysis for global superconvergence for integrodifferential equations. Appl. Math. 42 (1997), 1–21. DOI 10.1023/A:1022264125558 | MR 1426677
[10] Y. Lin: Galerkin methods for nonlinear Sobolev equations. Aequations Math. 40 (1990), 54–56. DOI 10.1007/BF02112280 | MR 1055190 | Zbl 0734.65078
[11] Y. Lin, T. Zhang: Finite element methods for nonlinear Sobolev equations with nonlinear boundary conditions. J. Math. Anal. & Appl. 165 (1992), 180–191. DOI 10.1016/0022-247X(92)90074-N | MR 1151067
[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. DOI 10.1137/0728056 | MR 1111453
[13] M. Nakao: Error estimates of a Galerkin method for some nonlinear Sobolev equations in one space dimension. Numer. Math. 47 (1985), 139–157. DOI 10.1007/BF01389881 | MR 0797883 | Zbl 0575.65112
[14] L. Wahlbin: Error estimates for a Galerkin method for a class of model equations for long waves. Numer. Math. 23 (1975), 289–303. DOI 10.1007/BF01438256 | MR 0388799 | Zbl 0283.65052
[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. DOI 10.1137/0710062 | MR 0351124
[16] Q. Zhu, Q. Lin: Superconvergence Theory of the Finite Element Methods. Hunan Science Press, 1990.
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