A posteriori error estimates for parabolic differential systems solved by the finite element method of lines

Karel Segeth

Applications of Mathematics (1994)

  • Volume: 39, Issue: 6, page 415-443
  • ISSN: 0862-7940

Abstract

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Systems of parabolic differential equations are studied in the paper. Two a posteriori error estimates for the approximate solution obtained by the finite element method of lines are presented. A statement on the rate of convergence of the approximation of error by estimator to the error is proved.

How to cite

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Segeth, Karel. "A posteriori error estimates for parabolic differential systems solved by the finite element method of lines." Applications of Mathematics 39.6 (1994): 415-443. <http://eudml.org/doc/32895>.

@article{Segeth1994,
abstract = {Systems of parabolic differential equations are studied in the paper. Two a posteriori error estimates for the approximate solution obtained by the finite element method of lines are presented. A statement on the rate of convergence of the approximation of error by estimator to the error is proved.},
author = {Segeth, Karel},
journal = {Applications of Mathematics},
keywords = {a posteriori error estimate; system of parabolic equations; finite element method; method of lines; method of lines; Schwarz inequality; local error indicator; a posteriori error estimates; finite element; system of parabolic equations},
language = {eng},
number = {6},
pages = {415-443},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A posteriori error estimates for parabolic differential systems solved by the finite element method of lines},
url = {http://eudml.org/doc/32895},
volume = {39},
year = {1994},
}

TY - JOUR
AU - Segeth, Karel
TI - A posteriori error estimates for parabolic differential systems solved by the finite element method of lines
JO - Applications of Mathematics
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 39
IS - 6
SP - 415
EP - 443
AB - Systems of parabolic differential equations are studied in the paper. Two a posteriori error estimates for the approximate solution obtained by the finite element method of lines are presented. A statement on the rate of convergence of the approximation of error by estimator to the error is proved.
LA - eng
KW - a posteriori error estimate; system of parabolic equations; finite element method; method of lines; method of lines; Schwarz inequality; local error indicator; a posteriori error estimates; finite element; system of parabolic equations
UR - http://eudml.org/doc/32895
ER -

References

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  6. 10.1145/1218052.1218054, ACM SIGNUM Newsletter 15 (1980), 10–11. (1980) DOI10.1145/1218052.1218054
  7. Finite Elements: Mathematical Aspects, Vol. 4, Englewood Cliffs, NJ, Prentice-Hall, 1983. (1983) MR0767804
  8. A Description of DDASSL: A Differential/Algebraic System Solver, Sandia Report No. Sand 82-8637, Livermore, CA, Sandia National Laboratory, 1982. (1982) MR0751605
  9. Finite Element Analysis, New York, J. Wiley & Sons, 1991. (1991) MR1164869
  10. 10.2307/2006222, Math. Comp. 34 (1980), 93–113. (1980) MR0551292DOI10.2307/2006222
  11. Finite Element Analysis and Applications, Chichester, J. Wiley & Sons, 1985. (1985) MR0817440

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