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A linear regularization method for a parameter identification problem in heat equation
Mondal Subhankar
Published in Walter de Gruyter GmbH
2020
Volume: 28

Issue: 2
Pages: 251 - 273
Abstract

Recently, Nair and Roy (2017) considered a linear regularization method for a parameter identifica-tion problem in an elliptic PDE. In this paper, we consider similar procedure for identifying the diffusion coef-ficient in the heat equation, modifying the Sobolev spaces involved appropriately. We derive error estimatesunder appropriate conditions and also consider the finite-dimensional realization of the method, which isessential for practical application. In the analysis of finite-dimensional realization, we give a procedure toobtain finite-dimensional subspaces of an infinite-dimensional Hilbert spaceL2(0,T;H1(Ω))by doing dou-ble discretization, that is, discretization corresponding to both the space and time domain. Also, we analyzethe parameter choice strategy and obtain an a posteriori parameter which is order optimal.