| Title:
|
Error estimates for distributed parameter identification in parabolic problems with output least squares and Crank-Nicolson method (English) |
| Author:
|
Kärkkäinen, Tommi |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
42 |
| Issue:
|
4 |
| Year:
|
1997 |
| Pages:
|
259-277 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
parameter identification |
| Keyword:
|
parabolic problem |
| Keyword:
|
finite element method |
| Keyword:
|
Crank-Nicolson scheme |
| Keyword:
|
least squares method |
| Keyword:
|
heat equation |
| Keyword:
|
inverse problem |
| Keyword:
|
error bounds |
| MSC:
|
35B37 |
| MSC:
|
35K05 |
| MSC:
|
35R30 |
| MSC:
|
49N50 |
| MSC:
|
65M06 |
| MSC:
|
65M15 |
| MSC:
|
65M30 |
| MSC:
|
65M60 |
| idZBL:
|
Zbl 0902.65036 |
| idMR:
|
MR1453932 |
| DOI:
|
10.1023/A:1023012328209 |
| . |
| Date available:
|
2009-09-22T17:55:01Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134358 |
| . |
| Reference:
|
[1] S. C. Brenner and L. R. Scott: The Mathematical Theory of Finite Element Methods. Texts in Applied Mathematics.Springer-Verlag vol. 15, New York, 1994. MR 1278258 |
| Reference:
|
[2] P. G. Ciarlet: The Finite Element Method for Elliptic Problems.North-Holland, Amsterdam, 1978. Zbl 0383.65058, MR 0520174 |
| Reference:
|
[3] J. Douglas, Jr. and T. Dupont: Galerkin methods for parabolic equations with nonlinear boundary conditions.Numer. Math. 20 (1973), 213–237. MR 0319379, 10.1007/BF01436565 |
| Reference:
|
[4] G. Fairweather: Finite Element Galerkin Methods for Differential Equations, Lecture notes in pure and applied mathematics vol. 34.Marcel Dekker, Inc., New York, 1978. MR 0495013 |
| Reference:
|
[5] R. S. Falk: Error estimates for the numerical identification of a variable coefficient.Math. Comp. 40 (1983), 537–546. Zbl 0551.65083, MR 0689469, 10.1090/S0025-5718-1983-0689469-3 |
| Reference:
|
[6] T. Kärkkäinen: Error Estimates for Distributed Parameter Identification Problems.PhD thesis, University of Jyäskylä, Department of Mathematics, Report 65, 1995. MR 1332491 |
| Reference:
|
[7] M. Luskin and R. Rannacher: On the smoothing property of the Galerkin method for parabolic equations.SIAM J. Numer. Anal. 19 (1981), 93–113. MR 0646596 |
| Reference:
|
[8] R. Scott: Interpolated boundary conditions in the finite element method.SIAM J. Numer. Anal. 12 (1975), 404–427. Zbl 0357.65082, MR 0386304, 10.1137/0712032 |
| Reference:
|
[9] X.-C. Tai and T. Kärkkäinen: Identification of a nonlinear parameter in a parabolic equation from a linear equation.Comp. Appl. Math. 14 (1995), 157–184. MR 1364156 |
| Reference:
|
[10] V. Thomée: Galerkin Finite Element Methods for Parabolic Problems, Lecture Notes in Mathematics vol. 1054.Springer-Verlag, Berlin Heidelberg, 1984. MR 0744045 |
| Reference:
|
[11] M. F. Wheeler: A priori $L^2$ error estimates for Galerkin approximations to parabolic partial differential equations.SIAM J. Numer. Anal. 10 (1973), 723–759. MR 0351124, 10.1137/0710062 |
| . |
