NUMERICAL APPROXIMATION OF THE FINAL STATE OF AN INCOMPLETE DATA HEAT PROBLEM
Keywords:
inverse problem, non-standard problem, adjoint problem, spectral method.DOI:
https://doi.org/10.17654/0974324323012Abstract
We determine the state at an instant $T_0$ of a 2D heat problem whose initial condition is partially known on a part of the domain. We use a non-standard method to solve this problem numerically.
Received: April 27, 2023
Accepted: May 29, 2023
References
A. F. Bennett, Inverse Modeling of the Ocean and Atmosphere, Cambridge University Press, Cambridge, 2002.
Abani Maidaoua Ali, Dia Bassirou, Diop Oulimata, Sembene Ama Diop Niang and Benjamin Mampassi, Solving an incomplete data inverse problem by a pseudo-spectral approximation method with a non standard approach, International Journal of Numerical Methods and Applications 18(2) (2019), 9-21.
K. J. Beven and J. Freer, Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology, Journal of Hydrology 249 (2001), 11-29.
D. H. Burn and D. B. Boorman, Estimation of hydrological parameters at ungauged catchments, Journal of Hydrology 143 (1992), 429-454.
D. G. Cacuci, Sensitivity theory for nonlinear systems: I. Nonlinear functional analysis approach, J. Math. Phys. 22 (1981), 2794-2802.
D. G. Cacuci, Sensitivity theory for nonlinear systems: II. Extensions to additional classes of responses, J. Math. Phys. 22 (1981), 2803-2812.
D. G. Cacuci, Sensitivity analysis, optimization, and global critical points, United States, 1989, pp. 602-603.
R. Daley, Atmospheric Data Analysis, Cambridge University Press, 1991.
Jacques Hadamard, On partial differential problems and their physical significance, Princeton University Bulletin, 1902, pp. 49-52.
E. Kalnay, S. Ki Park, Z.-X. Pu and J. Gao, Application of the quasi-inverse method to data assimilation, Month. Weather Rev. 128 (2000), 864-875.
L. S. Gandin, Objective Analysis of Meteorological Fields, Gidrometeorologicheskoe Izdatelstvo, Leningrad, 1963, Translation by Israel Program for Scientific Translations, Jerusalem, 1965, 242 pp.
Jean-Pierre Puel, A non standard approach to a data assimilation problem and Tychonov regularization revisited, SIAM J. Control Optim. 48(2) (2009), 1089-1111.
A. C. Lorenc, A global three-dimensional multivariate statistical interpolation scheme, Quart. J. Roy. Meteor. Soc. 109 (1981), 701-721.
D. Luenberger, Observers for multivariable systems, IEEE Trans. Automat. Control 11 (1966), 190-197.
O. Talagrand, Assimilation of observations, an introduction, J. Met. Soc. Japan 75(1B) (1997), 191-209.
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