Global error control for the continuous Galerkin finite element method for ordinary differential equations

Donald Estep; Donald French

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1994)

  • Volume: 28, Issue: 7, page 815-852
  • ISSN: 0764-583X

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Estep, Donald, and French, Donald. "Global error control for the continuous Galerkin finite element method for ordinary differential equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 28.7 (1994): 815-852. <http://eudml.org/doc/193761>.

@article{Estep1994,
author = {Estep, Donald, French, Donald},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {continuous Galerkin finite element method; error bounds; global error control; numerical experiments},
language = {eng},
number = {7},
pages = {815-852},
publisher = {Dunod},
title = {Global error control for the continuous Galerkin finite element method for ordinary differential equations},
url = {http://eudml.org/doc/193761},
volume = {28},
year = {1994},
}

TY - JOUR
AU - Estep, Donald
AU - French, Donald
TI - Global error control for the continuous Galerkin finite element method for ordinary differential equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1994
PB - Dunod
VL - 28
IS - 7
SP - 815
EP - 852
LA - eng
KW - continuous Galerkin finite element method; error bounds; global error control; numerical experiments
UR - http://eudml.org/doc/193761
ER -

References

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  1. [1] P. CIARLET, 1987, The Finite Element Method for Elliptic Problems. North-Holland, New York. Zbl0383.65058MR520174
  2. [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. Zbl0618.65104MR874731
  3. [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. Zbl0732.65093MR1083324
  4. [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. Zbl0830.65094MR1335652
  5. [5] K. ERIKSSON, C. JOHNSON, Adaptive finite element methods for parabolic problems III time steps variable in space, in preparation. 
  6. [6] K. ERIKSSON, C. JOHNSON, 1992, Adaptive finite element methods for parabolic problems IV nonlinear problems, Preprint # 1992-44, Chalmers Umversity of Technology. Zbl0835.65116MR1360457
  7. [7] K. ERIKSSON, C. JOHNSON, 1993, Adaptive finite element methods for parabolic problems V. long-time integration, preprint # 1993-04, Chalmers University of Technology. Zbl0835.65117MR1360458
  8. [8] D. ESTEP, A posteriori error bounds and global error control for approximations of ordinary differential equations, SIAM J. Numer. Anal. (to appear). Zbl0820.65052MR1313704
  9. [9] D. ESTEP, A. STUART, The dynamical behavior of the discontinuous Galerkin method and related difference schemes, preprint. Zbl0998.65080MR1898746
  10. [10] D. FRENCH, S. JENSEN, Long time behaviour ofarbitrary order continuous time Galerkin schemes for some one-dimensional phase transition problems, preprint. Zbl0806.65132MR1283945
  11. [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. [12] D. FRENCH, J. SCHAEFFER, 1990, Continuous finite element methods which preserve energy properties for nonlinear problems, Appl. Math. Comp., 39, 271-295. Zbl0716.65084MR1075255
  13. [13] J. HALE, 1980, Ordinary Differential Equations, John Wiley and Sons, Inc., New York. Zbl0186.40901MR587488
  14. [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. Zbl0661.65076MR954791
  15. [15] J. CHAEFFER, 1990, Personal communication. 
  16. [16] A. STROUD, 1974, Numerical Quadrature and Solution of Ordinary Differential Equations, Applied Mathematical Sciences 10, Springer-Verlag, New York, 1974. Zbl0298.65018MR365989

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