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, Tome 36 (1991) no. 2, pp. 123-133

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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 $L^\infty$ error estimates for finite element methods for parabolic integro-differential equations.
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.
DOI : 10.21136/AM.1991.104449
Classification : 45K05, 65M60, 65N30, 65R20
Keywords: Ritz-Volterra projection; stability; finite element; error estimates; initial- boundary-value problem; parabolic Volterra integro-differential equation
Lin, Yanping; Zhang, Tie. 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, Tome 36 (1991) no. 2, pp. 123-133. doi: 10.21136/AM.1991.104449
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[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, | DOI | MR

[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. | DOI | MR

[3] P. G. Ciarlet: The Finite Element Method for Elliptic Problems. North Holland, 1978. | MR | Zbl

[4] E. Green-Yanik G. Fairweather: Finite element methods for parabolic and hyperbolic partial integro-differential equations. to appear in Nonlinear Analysis. | MR

[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. | DOI | MR

[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

[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

[8] Qun Lin, Qi-ding Zhou: Superconvergence Theory of Finite Element Methods. Book to appear.

[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. | MR | Zbl

[10] R. Rannacher R. Scott: Some optimal error estimates for piecewise linear finite element approximations. Math. Соmр. 38 (1982) 437-445. | MR

[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

[12] R. Scott: Optimal $L^{\infty}$ estimates for the finite element on irregular meshes. Math. Соmр., 30 (1976) 681-697. | MR | Zbl

[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

[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. | DOI | MR

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