Global error control for the continuous Galerkin finite element method for ordinary differential equations
ESAIM: Modélisation mathématique et analyse numérique, Tome 28 (1994) no. 7, pp. 815-852.
@article{M2AN_1994__28_7_815_0,
     author = {Estep, Donald and French, Donald},
     title = {Global error control for the continuous {Galerkin} finite element method for ordinary differential equations},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {815--852},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {28},
     number = {7},
     year = {1994},
     mrnumber = {1309416},
     zbl = {0822.65054},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1994__28_7_815_0/}
}
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Estep, Donald; French, Donald. Global error control for the continuous Galerkin finite element method for ordinary differential equations. ESAIM: Modélisation mathématique et analyse numérique, Tome 28 (1994) no. 7, pp. 815-852. http://www.numdam.org/item/M2AN_1994__28_7_815_0/

[1] P. Ciarlet, 1987, The Finite Element Method for Elliptic Problems. North-Holland, New York. | MR | Zbl

[2] K. Eriksson, C. Johnson, 1987, Error estimates and automatic time step control for nonlinear parabolic problems, I, SIAM J. Numer. Anal., 24, 12-23. | MR | Zbl

[3] K. Eriksson, C. Johnson, 1991, Adaptive finite element methods for parabolic problems I a linear model problem, SIAM J. Numer. Anal., 28, 43-77. | MR | Zbl

[4] K. Eriksson, C. Johnson, 1992, Adaptive finite element methods for parabolic problems II optimal error estimates in L∞(L2) and L∞(L∞), preprint # 1992-09, Chalmers University of Technology. | MR | Zbl

[5] K. Eriksson, C. Johnson, Adaptive finite element methods for parabolic problems III time steps variable in space, in preparation.

[6] K. Eriksson, C. Johnson, 1992, Adaptive finite element methods for parabolic problems IV nonlinear problems, Preprint # 1992-44, Chalmers Umversity of Technology. | MR | Zbl

[7] K. Eriksson, C. Johnson, 1993, Adaptive finite element methods for parabolic problems V. long-time integration, preprint # 1993-04, Chalmers University of Technology. | MR | Zbl

[8] D. Estep, A posteriori error bounds and global error control for approximations of ordinary differential equations, SIAM J. Numer. Anal. (to appear). | MR | Zbl

[9] D. Estep, A. Stuart, The dynamical behavior of the discontinuous Galerkin method and related difference schemes, preprint. | MR | Zbl

[10] D. French, S. Jensen, Long time behaviour ofarbitrary order continuous time Galerkin schemes for some one-dimensional phase transition problems, preprint. | MR | Zbl

[11] D. French, S. Jensen, 1992, Global dynamics of finite element in time approximations to nonlinear evolution problems, International Conference on Innovative Methods in Numerical Analysis, Bressanone, Italy.

[12] D. French, J. Schaeffer, 1990, Continuous finite element methods which preserve energy properties for nonlinear problems, Appl. Math. Comp., 39, 271-295. | MR | Zbl

[13] J. Hale, 1980, Ordinary Differential Equations, John Wiley and Sons, Inc., New York. | MR | Zbl

[14] C. Johnson, 1988, Error estimates and adaptive time-step control for a class of one-step methods for stiff ordinary differential equations, SIAM J. Numer. Anal., 25, 908-926. | MR | Zbl

[15] J. Chaeffer, 1990, Personal communication.

[16] A. Stroud, 1974, Numerical Quadrature and Solution of Ordinary Differential Equations, Applied Mathematical Sciences 10, Springer-Verlag, New York, 1974. | MR | Zbl