Galerkin methods for a semilinear parabolic problem with nonlocal boundary conditions

Advances in Computational Mathematics

Volumn 6, Issue 1, 1996, Pages 243-262

  Fairweather, G ^a  

^a Department of Geology and Geological Engineering   (United States)

Author keywords

Crank Nicolson method; Extrapolated Crank Nicolson method; Finite element galerkin method; Nonlocal boundary conditions; Optimal error estimates; Semilinear parabolic problem

Indexed keywords

EID: 21444444197     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02127706     Document Type: Article

References (12)

1. W. A. Day, Extensions of a property of the heat equation to linear thermoelasticity and other theories, Quart. Appl. Math. 40 (1982) 319-330.
2. W. A. Day, A decreasing property of solutions of parabolic equations with applications to thermoelasticity, Quart. Appl. Math. 41 (1983) 468-475.
3. 2-approximation by splines in terms of a global mesh ratio, Math. Comp. 30 (1976) 765-771.
4. ∞ error estimates for Galerkin approximations to solutions of two-point boundary value problems, Math. Comp. 29 (1975) 475-483.
5. G. Ekolin, Finite difference methods for a nonlocal boundary value problem for the heat equation, BIT 31 (1991) 245-261.
6. A. Friedman, Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions, Quart. Appl. Math. 44 (1986) 401-407.
7. B. Kawohl, Remarks on a paper by W. A. Day on a maximum principle under nonlocal boundary conditions, Quart. Appl. Math. 44 (1987) 751-752.
8. Y. Lin, S. Xu and H.-C. Yin, Finite difference approximations for a class of non-local parabolic equations, Internat. J. Math. Math. Sci., to appear.
9. J. C. López-Marcos and J. M. Sanz-Serna, A definition of stability for nonlinear problems, in: Numerical Treatment of Differential Equations, ed. K. Strehmel, Teubner Texte zur Mathematik (Teubner, Leipzig, 1988) pp. 216-226.
10. J. C. López-Marcos and J. M. Sanz-Serna, Stability and convergence in numerical analysis III: Linear investigation of nonlinear stability, IMA J. Numer. Anal. 8 (1988) 71-84.
11. H. J. Stetter, Analysis of Discretization Methods for Ordinary Differential Equations (Springer, Berlin, 1973).
12. ∞ error estimate for Galerkin approximations to solutions of two point boundary value problems, SIAM J. Numer. Anal. 10 (1973) 914-917.