Error estimates and step-size control for the approximate solution of a first order evolution equation

Günter Lippold

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1991)

  • Volume: 25, Issue: 1, page 111-128
  • ISSN: 0764-583X

How to cite

top

Lippold, Günter. "Error estimates and step-size control for the approximate solution of a first order evolution equation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 25.1 (1991): 111-128. <http://eudml.org/doc/193616>.

@article{Lippold1991,
author = {Lippold, Günter},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {step-size control; first order evolution equation; backward Euler method; nonlinear monotone operator; Hilbert space; error bounds},
language = {eng},
number = {1},
pages = {111-128},
publisher = {Dunod},
title = {Error estimates and step-size control for the approximate solution of a first order evolution equation},
url = {http://eudml.org/doc/193616},
volume = {25},
year = {1991},
}

TY - JOUR
AU - Lippold, Günter
TI - Error estimates and step-size control for the approximate solution of a first order evolution equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1991
PB - Dunod
VL - 25
IS - 1
SP - 111
EP - 128
LA - eng
KW - step-size control; first order evolution equation; backward Euler method; nonlinear monotone operator; Hilbert space; error bounds
UR - http://eudml.org/doc/193616
ER -

References

top
  1. [1] O. AXELSSON, Error estimates over infinite intervals of some discretizations of evolution equations, BIT 24 (1984), 413-429 Zbl0573.65038MR764815
  2. [2] I. BABUŠKA and W. C. RHEINBOLDT, Error estimates for adaptive finite element computations, SIAM J Numer Anal 75 (1978), 736-754 Zbl0398.65069MR483395
  3. [3] M. BIETERMANN and I. BABUŠKA, An adaptive method of lines with error control for parabolic equations of the reaction-diffusion type, J Comp Phys 63 (1986), 33-66 Zbl0596.65084MR832563
  4. [4] K. ERICSSON, C. JOHNSON and V. THOMEE, Time discretization of par abolie problems by the discontinuons Galerkin method, M2AN 19 (1985), 611-643 Zbl0589.65070MR826227
  5. [5] H. GAJEWSKI, K. ROGER and K. ZACHARIAS, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie-Verlag, Berlin, 1974 Zbl0289.47029MR636412
  6. [6] K. GROGER, Discrete-time Galerkin methods for nonlinear evolution equations, Math Nachr 84 (1978), 247-275 Zbl0408.65071MR518126
  7. [7] C. JOHNSON, Y.-Y. NIE and V. THOMEE, An a posteriori error estimate for a backward Euler discretization of a parabolic problem, SIAM J Numer Anal, 27 (1990), 277-291 Zbl0701.65063MR1043607
  8. [8] J. KAČUR, Method of Rothe in evolution equations, Teubner Leipzig, 1985 Zbl0582.65084MR834176
  9. [9] J. L. LIONS and E. MAGENES, Problèmes aux limites non homogènes et applications I, Dunod, Paris, 1968 Zbl0165.10801
  10. [10] G. LIPPOLD, Adaptive approximation, ZAMM 67 (1987), 453-465 Zbl0652.65062MR919399
  11. [11] M. LUSKIN and R. RANNACHER, On the smoothing property of the Galerkin method for par abolic equations, SIAM J Numer Anal 19 (1981), 93-113 Zbl0483.65064MR646596
  12. [12] J. NEČAS, Application of Rothe's method to abstract parabohe equations, Czech Math J 24 (1974), 496-500 Zbl0311.35059MR348571
  13. [13] P. A. RAVIART, Sur l'approximation de certaines équations d'évolution linéaires et non linéaires, J Math Pures Appl 46 (1967), 11-107, 109-183 Zbl0198.49901
  14. [14] Th. REIHER, An adaptive method for linear parabolic partial differential equations, ZAMM 67 (1987), 557-565 Zbl0637.65118MR922260
  15. [15] E. ROTHE, Zweidimensionale parabolische Randwertaufgaben als Grenzfall eindimensionaler Randwertaufgaben, Math. Ann. 102 (1930), 650-670. MR1512599JFM56.1076.02
  16. [16] J. M. SANZ-SERNA and G. VERWER, Stability and convergence in the PDE/stiff ODE interphase, Report NM-R8619, Centre for Mathematics and Computer Science Amsterdam, 1986. Zbl0671.65078
  17. [17] V. THOMÉE and L. B. WAHLBIN, On Galerkin methods in semilinear parabolic problems, SIAM J. Numer. Anal. 12 (1975), 378-389. Zbl0307.35007MR395269
  18. [18] M. F. WHEELER, An H-1 Galerkin method for a parabolic problem in a single space variable, SIAM J. Numer. Anal. 12 (1975), 803-817. Zbl0331.65075MR413556

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.