Finite element methods with numerical quadrature for parabolic integrodifferential equations

SIAM Journal on Numerical Analysis

Volumn 33, Issue 3, 1996, Pages 1084-1105

  Pani, Amiya K ^a   Peterson, Todd E ^b  

^a INDIAN INSTITUTE OF TECHNOLOGY BOMBAY   (India)

^b GEORGE MASON UNIVERSITY   (United States)

Author keywords

Error estimate; Finite element; Integrodifferential equation; Nonsmooth data; Numerical quadrature; Parabolic

Indexed keywords

EID: 0001669214     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/0733053     Document Type: Article

References (13)

1. 1 projections and Galerkin methods for nonlinear parabolic integrodifferential equations, Calcolo, 25 (1988), pp. 187-201.
2. 2 error estimates for finite element methods for nonlinear diffusion equations with memory, SIAM J. Numer. Anal., 27 (1990), pp. 595-607.
3. C. M. CHEN AND V. THOMÉE, The lumped mass finite element method for a parabolic problem, J. Austral. Math. Soc. Ser. B, 26 (1985), pp. 329-354.
4. S. CHOU AND Q. LI, The effect of numerical integration infinite element methods for nonlinear parabolic equations, Numer. Methods Partial Differential Equations, 6 (1990), pp. 263-274.
5. D. ESTEP AND S. LARSSON, The Discontinuous Galerkin Method for Semilinear Parabolic Problems, Technical Report, Department of Mathematics, Chalmers University of Technology, Gothenburg, Sweden, 1991.
6. Y. LIN, V. THOMÉE, AND L. B. WAHLBIN, Ritz-Volterra projections to finite element spaces and applications to integro-differential and related equations, SIAM J. Numer. Anal., 28 (1991), pp. 1047-1070.
7. Y. LIN AND T. ZHANG, The stability of Ritz- Volterra projections and error estimates for finite element methods for a class of integro-differential equations of parabolic type, Appl. Math., 36 (1991), pp. 123-133.
8. Y. NIE AND V. THOMÉE, A lumped mass finite-element method with quadrature for a non-linear parabolic problem, IMA J. Numer. Anal., 5 (1985), pp. 371-396.
9. A. K. PANI, V. THOMÉE, AND L. B. WAHLBIN, Numerical methods for hyperbolic and parabolic integrodifferential equations, J. Integral Equations Appl., 4 (1992), pp. 533-584.
10. P. A. RAVIART, The use of numerical integration infinite element methods for solving parabolic equations, in Topics in Numerical Analysis, Academic Press, New York, 1973.
11. M. L. ROUX AND V. THOMÉE, Numerical Solution of Semilinear Integro-Differential Equations of Parabolic Type with Nonsmooth Data, Technical Report, Department of Mathematics, Chalmers University of Technology, Gothenburg, Sweden, 1987.
12. V. THOMÉE, J. XU, AND N. ZHANG, Superconvergence of the gradient in piecewise linear finite-element approximation to a parabolic problem, SIAM J. Numer. Anal., 26 (1989) pp. 553-573.
13. V. THOMÉE AND N. ZHANG, Error estimates for semidiscrete finite element methods for parabolic integrodifferential equations. Math. Comp., 53 (1989), pp. 121-139.