Discrete methods in the study of an inverse problem for Laplace's equation期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Discrete methods in the study of an inverse problem for Laplace's equation

Authors:	Fasino, D Inglese, G

Affiliation:	^A1 Dipartimento di Matematica e Informatica, University of Udine, Udine, Italy ^A2 Istituto di Analisi Globale e Applicazioni, CNR, Firenze, Italy

Abstract:	Let u be harmonic in the interior of a rectangle ${Omega}$ and satisfythe third-kind boundary condition u_n + yu = ${Phi}$ where ${Phi}$ $>=$ 0, y $>=$ 0with supports included in the bottom and in the top side of ${Omega}$ , respectively. Recovering y from a knowledge of ${Phi}$ and of thetrace of u on the bottom ${Omega}$ is a nonlinear inverse problem ofinterest in the field of nondestructive evaluation. A convergentGalerkin method for approximating y is proposed and tested innumerical experiments.

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