Inversion of Robin coefficient by a spectral stochastic finite element approach

Authors:
Bangti Jin;Jun Zou
Affiliations:
Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong;Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
Venue:
Journal of Computational Physics
Year:
2008

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Abstract

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method using polynomial chaos is utilized for the discretization of the optimization problem, and its convergence is analyzed. The nonlinear conjugate gradient method is derived for the optimization system. Numerical results for several two-dimensional problems are presented to illustrate the accuracy and efficiency of the stochastic finite element method.