A numerical approach for the determination of a missing boundary data in elliptic problems

We consider the problem of the recovery of an unknown transfer coefficient in the Robin boundary condition on an inaccessible part of the boundary of an elliptic boundary value problem. The physical process inside the domain is governed by a linear elliptic equation of second order. The unknown boundary data are determined from superfluous information on the accessible part of the boundary. We show that the inverse problem is equivalent to a system of direct problems. We design a numerical approach for thin domains. The method is tested by numerical experiments.

[2]  Roger Van Keer,et al.  Determination of a Robin coefficient in semilinear parabolic problems by means of boundary measurements , 2002 .

[3]  Diego A. Murio,et al.  Recovery of the transient heat transfer coefficient in the nonlinear boundary value problem for the heat equation , 1993 .

[4]  On an Inverse Problem of Pressure Recovery Arising from Soil Venting Facilities , 2001, Appl. Math. Comput..

[5]  Identification of transmissivity coefficients by mollification techniques. Part II: n-dimensional elliptic problems , 1995 .

[6]  Fadil Santosa,et al.  A Method for Imaging Corrosion Damage in Thin Plates from Electrostatic Data , 1995 .

[7]  Diego A. Murio,et al.  IDENTIFICATION OF TRANSMISSIVITY COEFFICIENTS BY MOLLIFICATION TECHNIQUES. PART I: ONE-DIMENSIONAL ELLIPTIC AND PARABOLIC PROBLEMS , 1993 .

[8]  D. Arnold,et al.  Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates , 1985 .

[9]  Kurt Bryan,et al.  Stability and reconstruction for an inverse problem for the heat equation , 1998 .

[10]  G. Inglese,et al.  An inverse problem in corrosion detection , 1997 .

[11]  S. Kabanikhin,et al.  Optimizational method for solving the Cauchy problem for an elliptic equation , 1995 .

[12]  Michael V. Klibanov,et al.  A computational quasi-reversiblility method for Cauchy problems for Laplace's equation , 1991 .

[13]  Roger Van Keer,et al.  Determination of the convective transfer coefficient in elliptic problems from a non-standard boundary condition , 2000 .

[14]  On the determination of an unknown boundary function in a parabolic equation , 1999 .

[15]  Dario Fasino,et al.  An inverse Robin problem for Laplace's equation: theoretical results and numerical methods , 1999 .

[16]  Discrete methods in the study of an inverse problem for Laplace's equation , 1999 .