Variational data assimilation for a nonstationary heat conduction problem with nonlinear diffusion

Russian Journal of Numerical Analysis and Mathematical Modelling

Volumn 20, Issue 1, 2005, Pages 81-95

  Parmuzin, E I ^a   Shutyaev, V P ^a  

^a INSTITUTE OF NUMERICAL MATHEMATICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DATA REDUCTION; DIFFERENTIAL EQUATIONS; DIFFUSION; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; OCEANOGRAPHY; PROBLEM SOLVING;

DATA ASSIMILATION; HEAT EXCHANGE; NONLINEAR DIFFUSION; NUMERICAL PROBLEMS;

HEAT CONDUCTION;

EID: 14844359024     PISSN: 09276467     EISSN: None     Source Type: Journal    
DOI: 10.1163/1569398053270804     Document Type: Article

References (14)

1. V. I. Agoshkov, Methods of Optimal Control and Adjoint Equations in Problems of Mathematical Physics. Inst. of Numer. Math., Russ. Acad. Sci., Moscow, 2003 (in Russian).
2. V. I. Agoshkov and G. I. Marchuk, On solvability and numerical solution of data assimilation problems. Russ. J. Numer. Anal. Math. Modelling (1993) 8, No. 1, 1-16.
3. F.-X. Le Dimet and V. P. Shutyaev, On data assimilation for quasilinear parabolic problems. Russ. J. Numer. Anal. Math. Modelling (2001) 16, No. 3, 247-259.
4. Kh. Gaevsky, K. Gröger, and K. Zakharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Akademie-Verlag, Berlin, 1974 (in German).
5. Chr. Kazantsev, S. N. Moshonkin, and V. B. Zalesny, Mathematical modelling of the global ocean dynamics: solvability, numerical algorithm, calculations. In: Variability and Predictability of Atmospheric and Oceanic Circulations. MGU, Moscow, 1999.
6. J.-L. Lions, Optimal Control by Systems Described by Partial Differential Equations. Mir, Moscow, 1972.
7. G. I. Marchuk, V. I. Agoshkov, and V. P. Shutyaev, Adjoint Equations and Perturbation Algorithms in Nonlinear Problems. CRC Press, New York, 1996.
8. G. I. Marchuk and V. B. Zalesny, A numerical technique for geophysical data assimilation problem using Pontryagins principle and splitting-up method. Russ. J. Numer. Anal. Math. Modelling (1993) 8, No. 4, 311-326.
9. G. I. Marchuk and V. P. Shutyaev, Iteration methods for solving a data assimilation problem. Russ. J. Numer. Anal. Math. Modelling (1994) 9, No. 3, 265-279.
10. G. Marchuk, V. Shutyaev, and V. Zalesny, Approaches to the solution of data assimilation problems. In: Optimal Control and Partial Differential Equations. IOS Press, Amsterdam, 2001, pp. 489-497.
11. G. A. Schmidt and L. A. Mysak, The stability of a zonally averaged thermohaline circulation model. Tellus (1996) 48A, 158-178.
12. V. P. Shutyaev, Data assimilation problem for locally ID vertical heat exchange model. In: Proc. INM RAS on scientific activity in 2001. Theses of scientific talks at the current session. Inst. of Numer. Math., Russ. Acad. Sci., Moscow, 2001, pp. 69-70 (in Russian).
13. V. P. Shytyaev, Control Operators and Iterative Algorithms in Variational Data Assimilation Problem. Nauka, Moscow, 2001.
14. M. Ventsel and V. B. Zalesny, Data assimilation in ID heat convection-diffusion model in the ocean. Atmos. Ocean Phys. (1996) 32, No. 5, 613-629.