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An Analytical Method for the Inverse Cauchy Problem of Laplace Equation in a Rectangular Plate

Published online by Cambridge University Press:  07 December 2011

C.-S. Liu
C.-S. Liu*
Affiliation:
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
*Professor, corresponding author (E-mail: liucs@ntu.edu.tw)
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Abstract

The present paper reveals an analytically computational method for the inverse Cauchy problem of Laplace equation. For the sake of analyticity, and also for the frequent use of rectangular plate in engineering structure, we only consider the analytical solution in a two-dimensional rectangular domain, wherein a missing boundary condition is recovered from a partial measurement of the Neumann data on an accessible boundary. The Fourier series is used to formulate a first-kind Fredholm integral equation for the unknown function of data. Then, we consider a Lavrentiev regularization amended to a second-kind Fredholm integral equation. The termwise separable property of kernel function allows us to obtain a closed-form solution of the regularization type. The uniform convergence and error estimation of the regularization solution are proven. The numerical examples show the effectiveness and robustness of the new method.

Keywords

Laplace equationInverse Cauchy problemFourier seriesAnalytical regularization solutionError estimationSeparable kernelLavrentiev regularization
Type
Articles
Information
Journal of Mechanics , Volume 27 , Issue 4 , December 2011 , pp. 575 - 584
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2011

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