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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  2. A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems, Numer. Math. 65 (1993), 1–21. (1993) MR1217436
  3. A posteriori error estimates for the finite element method, Internat. J. Numer. Methods Engrg. 12 (1978), 1597–1615. (1978) 
  4. The finite element method for parabolic equations I, II, Numer. Math. 40 (1982), 339–371, 373–406. (1982) 
  5. Matrix Theory, Moskva, Nauka, 1966. (Russian) (1966) 
  6. LSODE and LSODI, two new initial value ordinary differential equation solvers, ACM SIGNUM Newsletter 15 (1980), 10–11. (1980) 
  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. Negative norm estimates and superconvergence in Galerkin methods for parabolic problems, Math. Comp. 34 (1980), 93–113. (1980) MR0551292
  11. Finite Element Analysis and Applications, Chichester, J. Wiley & Sons, 1985. (1985) MR0817440

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