Fully discrete error estimation by the method of lines for a nonlinear parabolic problem

Tomáš Vejchodský

Applications of Mathematics (2003)

  • Volume: 48, Issue: 2, page 129-151
  • ISSN: 0862-7940

Abstract

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A posteriori error estimates for a nonlinear parabolic problem are introduced. A fully discrete scheme is studied. The space discretization is based on a concept of hierarchical finite element basis functions. The time discretization is done using singly implicit Runge-Kutta method (SIRK). The convergence of the effectivity index is proven.

How to cite

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Vejchodský, Tomáš. "Fully discrete error estimation by the method of lines for a nonlinear parabolic problem." Applications of Mathematics 48.2 (2003): 129-151. <http://eudml.org/doc/33140>.

@article{Vejchodský2003,
abstract = {A posteriori error estimates for a nonlinear parabolic problem are introduced. A fully discrete scheme is studied. The space discretization is based on a concept of hierarchical finite element basis functions. The time discretization is done using singly implicit Runge-Kutta method (SIRK). The convergence of the effectivity index is proven.},
author = {Vejchodský, Tomáš},
journal = {Applications of Mathematics},
keywords = {a posteriori error estimates; finite elements; nonlinear parabolic problems; effectivity index; singly implicit Runge-Kutta methods (SIRK); a posteriori error estimates; finite elements},
language = {eng},
number = {2},
pages = {129-151},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Fully discrete error estimation by the method of lines for a nonlinear parabolic problem},
url = {http://eudml.org/doc/33140},
volume = {48},
year = {2003},
}

TY - JOUR
AU - Vejchodský, Tomáš
TI - Fully discrete error estimation by the method of lines for a nonlinear parabolic problem
JO - Applications of Mathematics
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 2
SP - 129
EP - 151
AB - A posteriori error estimates for a nonlinear parabolic problem are introduced. A fully discrete scheme is studied. The space discretization is based on a concept of hierarchical finite element basis functions. The time discretization is done using singly implicit Runge-Kutta method (SIRK). The convergence of the effectivity index is proven.
LA - eng
KW - a posteriori error estimates; finite elements; nonlinear parabolic problems; effectivity index; singly implicit Runge-Kutta methods (SIRK); a posteriori error estimates; finite elements
UR - http://eudml.org/doc/33140
ER -

References

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  10. High-order adaptive solution of parabolic equations  I. Singly implicit Runge-Kutta methods and error estimation, Rensselaer Polytechnic Institute Report 91-12, Troy, NY, Department of Computer Science, Rensselaer Polytechnic Institute, 1991. (1991) 
  11. 10.1007/BF01989753, BIT 33 (1993), 309–331. (1993) MR1326022DOI10.1007/BF01989753
  12. Nonlinear differential equations and inequalities, Mathematical Institute of Charles University, Prague, in preparation. 
  13. 10.1007/s002110050459, Numer. Math. 33 (1999), 455–475. (1999) Zbl0936.65113MR1715561DOI10.1007/s002110050459
  14. Finite Element Analysis, John Wiley & Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore, 1991. (1991) MR1164869
  15. Galerkin Finite Element Methods for Parabolic Problems, Springer, Berlin, 1997. (1997) MR1479170

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