NUMERICALLY SOLVING THE IDENTIFICATION PROBLEM FOR THE LOWER COEFFICIENT OF A PARABOLIC EQUATION
Аннотация
In the theory and practice of inverse problems for partial differential equations (PDEs) much attention is paid to the identification problem of coefficients from some additional information. This article deals with the problem of determining in a multidimensional parabolic equation the lower coefficient that depends only on time. To solve numerically a nonlinear inverse problem, linearized approximations in time are constructed using standard finite element procedures in space. The computational algorithm is based on a special decomposition, where the transition to a new time level is implemented via solving two standard elliptic problems. The numerical results presented here for a model 2D problem demonstrate capabilities of the proposed computational algorithms for approximate solving inverse problems.
Ключевые слова
inverse problem,
identification of the coefficient,
parabolic partial differential equation,
finite element approximation,
difference scheme
При поддержке: The authors were supported by the Russian Foundation for Basic Research (Grants 13–01– 00719 and 14–01–00785).
Об авторах
P. N. Vabishchevich
Nuclear Safety Institute, Russian Academy of Sciences
Россия
Россия
P. N. Vabishchevich
Nuclear Safety Institute, Russian Academy of Sciences 115191, Moscow, Russia
V. I. Vasil′ev
North-Eastern Federal University
Россия
Россия
V. I. Vasil′ev
North-Eastern Federal University, 677000, Yakutsk, Russia
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Рецензия
Для цитирования:
Vabishchevich P.N., Vasil′ev V.I. NUMERICALLY SOLVING THE IDENTIFICATION PROBLEM FOR THE LOWER COEFFICIENT OF A PARABOLIC EQUATION. Математические заметки СВФУ. 2014;21(4):71-87.
For citation:
Vabishchevich P.N., Vasil′ev V.I. NUMERICALLY SOLVING THE IDENTIFICATION PROBLEM FOR THE LOWER COEFFICIENT OF A PARABOLIC EQUATION. Mathematical notes of NEFU. 2014;21(4):71-87. (In Russ.)
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