Geodesic
Error estimates for distributed parameter identification in parabolic problems with output least squares and Crank-Nicolson method
Applications of Mathematics, Tome 42 (1997) no. 4, pp. 259-277.

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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.
DOI : 10.1023/A:1023012328209
Classification : 35B37, 35K05, 35R30, 49N50, 65M06, 65M15, 65M30, 65M60
Keywords: parameter identification; parabolic problem; finite element method; Crank-Nicolson scheme; least squares method; heat equation; inverse problem; error bounds 
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     title = {Error estimates for distributed parameter identification in parabolic problems with output least squares and {Crank-Nicolson} method},
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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, Tome 42 (1997) no. 4, pp. 259-277. doi : 10.1023/A:1023012328209. http://geodesic.mathdoc.fr/articles/10.1023/A:1023012328209/

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