Error estimates for distributed parameter identification in parabolic problems with output least squares and Crank-Nicolson method

Tommi Kärkkäinen

Applications of Mathematics (1997)

  • Volume: 42, Issue: 4, page 259-277
  • ISSN: 0862-7940

Abstract

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The identification problem of a functional coefficient in a parabolic equation is considered. For this purpose an output least squares method is introduced, and estimates of the rate of convergence for the Crank-Nicolson time discretization scheme are proved, the equation being approximated with the finite element Galerkin method with respect to space variables.

How to cite

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Kärkkäinen, Tommi. "Error estimates for distributed parameter identification in parabolic problems with output least squares and Crank-Nicolson method." Applications of Mathematics 42.4 (1997): 259-277. <http://eudml.org/doc/32981>.

@article{Kärkkäinen1997,
abstract = {The identification problem of a functional coefficient in a parabolic equation is considered. For this purpose an output least squares method is introduced, and estimates of the rate of convergence for the Crank-Nicolson time discretization scheme are proved, the equation being approximated with the finite element Galerkin method with respect to space variables.},
author = {Kärkkäinen, Tommi},
journal = {Applications of Mathematics},
keywords = {parameter identification; parabolic problem; finite element method; Crank-Nicolson scheme; least squares method; heat equation; inverse problem; error bounds; parameter identification; least squares method; finite element method; Crank-Nicolson scheme; heat equation; inverse problem; error bounds},
language = {eng},
number = {4},
pages = {259-277},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Error estimates for distributed parameter identification in parabolic problems with output least squares and Crank-Nicolson method},
url = {http://eudml.org/doc/32981},
volume = {42},
year = {1997},
}

TY - JOUR
AU - Kärkkäinen, Tommi
TI - Error estimates for distributed parameter identification in parabolic problems with output least squares and Crank-Nicolson method
JO - Applications of Mathematics
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 42
IS - 4
SP - 259
EP - 277
AB - The identification problem of a functional coefficient in a parabolic equation is considered. For this purpose an output least squares method is introduced, and estimates of the rate of convergence for the Crank-Nicolson time discretization scheme are proved, the equation being approximated with the finite element Galerkin method with respect to space variables.
LA - eng
KW - parameter identification; parabolic problem; finite element method; Crank-Nicolson scheme; least squares method; heat equation; inverse problem; error bounds; parameter identification; least squares method; finite element method; Crank-Nicolson scheme; heat equation; inverse problem; error bounds
UR - http://eudml.org/doc/32981
ER -

References

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  2. The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. (1978) Zbl0383.65058MR0520174
  3. 10.1007/BF01436565, Numer. Math. 20 (1973), 213–237. (1973) MR0319379DOI10.1007/BF01436565
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  5. 10.1090/S0025-5718-1983-0689469-3, Math. Comp. 40 (1983), 537–546. (1983) Zbl0551.65083MR0689469DOI10.1090/S0025-5718-1983-0689469-3
  6. Error Estimates for Distributed Parameter Identification Problems, PhD thesis, University of Jyäskylä, Department of Mathematics, Report 65, 1995. (1995) MR1332491
  7. On the smoothing property of the Galerkin method for parabolic equations, SIAM J. Numer. Anal. 19 (1981), 93–113. (1981) MR0646596
  8. 10.1137/0712032, SIAM J. Numer. Anal. 12 (1975), 404–427. (1975) Zbl0357.65082MR0386304DOI10.1137/0712032
  9. Identification of a nonlinear parameter in a parabolic equation from a linear equation, Comp. Appl. Math. 14 (1995), 157–184. (1995) MR1364156
  10. Galerkin Finite Element Methods for Parabolic Problems, Lecture Notes in Mathematics vol. 1054, Springer-Verlag, Berlin Heidelberg, 1984. (1984) MR0744045
  11. 10.1137/0710062, SIAM J. Numer. Anal. 10 (1973), 723–759. (1973) MR0351124DOI10.1137/0710062

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