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integrodifferential equations; global superconvergence; immediate analysis; postprocessing; finite element method; parabolic; hyperbolic
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.
[1] J. Cannon, Y. Lin: A Galerkin procedure for diffusion equations with boundary integral conditions. Int. J. Eng. Sci. 28 (1990), 579–587. DOI 10.1016/0020-7225(90)90087-Y | MR 1059777
[2] M. Křížek, P. Neittaanmäki: On Finite Element Approximation of Variational Problems and Applications. Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific & Technical, Essex, 1989. MR 1066462
[3] Q. Lin: A new observation in FEM. Proc. Syst. Sci. & Syst. Eng., Great Wall (H.K.), Culture Publish Co., 1991, pp. 389–391.
[4] Q. Lin, N. Yan, A. Zhou: A rectangle test for interpolated finite elements, ibid. 217–229.
[5] Q. Lin, Q. Zhu: The Preprocessing and Postprocessing for the Finite Element Method. Shanghai Scientific & Technical Publishers, 1994.
[6] Y. Lin: Galerkin methods for nonlinear parabolic integrodifferential equations with nonlinear boundary conditions. SIAM J. Numer. Anal. 27 (1990), 608–621. DOI 10.1137/0727037 | MR 1041254 | Zbl 0703.65095
[7] Y. Lin, T. Zhang: 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. MR 1097696
[8] 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
[9] V. Thomée: Galerkin Finite Element Methods for Parabolic Problems. Lect. Notes in Math., 1054, 1984. MR 0744045
[10] V. Thomée, J. Xu, N. Zhang: Superconvergence of the gradient in piecewise linear finite element approximation to a parabolic problem. SIAM J. Numer. Anal. 26 (1989), 553–573. DOI 10.1137/0726033 | MR 0997656
[11] V. Thomée, N. Zhang: Error estimates for semidiscrete finite element methods for parabolic integrodifferential equations. Math. Comp. 53 (1989), 121–139. DOI 10.2307/2008352 | MR 0969493
[12] 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
[13] Q. Zhu, Q. Lin: Superconvergence Theory of the Finite Element Methods. Hunan Science Press, 1990.
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