L∞(L2) and L∞(L∞) error estimates for mixed methods for integro-differential equations of parabolic type

Mathematical Modelling and Numerical Analysis

Volumn 33, Issue 3, 1999, Pages 531-546

  Jiang, Ziwen ^a  

^a SHANDONG NORMAL UNIVERSITY   (China)

Author keywords

Error estimates; Integro differential equations; Mixed finite element; Parabolic type

Indexed keywords

EID: 0038932835     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:1999151     Document Type: Article

References (16)

1. 2 error estimates for finite-element methods for nonlinear diffusion equations with memory. SIAM J. Numer. Anal. 27 (1990) 595-607.
2. 1 projection and Galerkin methods for nonlinear parabolic integro-differential equations. Calcolo 25 (1988) 187-201.
3. L.C. Cowsar, T.F. Dupont and M.F. Wheeler, A priori estimates for mixed finite element methods for the wave equations. Comput. Methods Appl. Mech. Engrg. 82 (1990) 205-222.
4. L.C. Cowsar, T.F. Dupont and M.F. Wheeler, A priori estimates for mixed finite element approximations of second-order hyperbolic equations with absorbing boundary conditions. SIAM J. Numer. Anal. 33 (1996) 492-504.
5. J. Douglas Jr. and J.E. Roberts, Global estimates for mixed methods for second order elliptic equations. Math. Comp. 44 (1985) 39-52.
6. E. Greenwell-Yanik and G. Fairweather, Finite element methods for parabolic and hyperbolic partial integro-differential equations. Nonlinear Anal. 12 (1988) 785-809.
7. M.N. Le Roux and V. Thomée, Numerical solution of semilinear integro-differential equations of parabolic type with nonsmooth data. SIAM J. Numer. Anal 26 (1989) 1291-1309.
8. Y. Lin. Galerkin methods for nonlinear parabolic integro-differential equations with nonlinear boundary conditions. SIAM J. Numer. Anal. 27 (1990) 608-621.
9. F.A. Milner, Mixed finite element methods for Quasilinear second-order elliptic problems. Math. Comp. 44 (1985) 303-320.
10. F.A. Milner and E.-J. Park, A mixed finite element method for a strongly nonlinear second-order elliptic problem. Math. Comp. 64 (1995) 973-988.
11. E.J. Park, Mixed finite element method for nonlinear second-order elliptic problems. SIAM J. Numer. Anal. 32 (1995) 865-885.
12. P.A. Raviart and J.M. Thomas, A mixed finite element method for 2-nd order elliptic problems, in Mathematical Aspects of the Finite Element Method. Lect. Notes Math. 606 (1977) 292-315.
13. ∞-estimates for a mixed finite element method for second order elliptic and parabolic problems. Calcolo 20 (1983) 355-377.
14. J. Squeff, Superconvergence of mixed finite element methods for parabolic equations. RAIRO Modél. Math. Anal. Numér. 21 (1987) 327-352.
15. V. Thomée and N.Y. Zhang, Error estimates for semi-discrete finite element methods for parabolic integro-differential equations. Math. Comp. 53 (1989) 121-139.
16. ∞-error estimates for mixed finite element methods for second order elliptic problems. Numer. Math. 55 (1989) 401-430.