A procedure for the temperature reconstruction in corner domains from Cauchy data

T. Johansson, L. Marin

Research output: Contribution to journal › Article

Abstract

An iterative procedure is proposed for the reconstruction of a stationary temperature field from Cauchy data given on a part of the boundary of a bounded plane domain where the boundary is smooth except for a finite number of corner points. In each step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. Convergence is proved in a weighted L2-space. Numerical results are included which show that the procedure gives accurate and stable approximations in relatively few iterations.
Original languageEnglish
Pages (from-to)357-372
Number of pages16
JournalInverse Problems
Volume23
Issue number1
DOIs
Publication statusPublished - 17 Jan 2007

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Cauchy
Boundary value problems
Mathematical operators
Temperature distribution
Weighted Spaces
Iterative Procedure
Temperature Field
Heat
Boundary Value Problem
Iteration
Numerical Results
Temperature
Series
Approximation
Operator
Hot Temperature

Keywords

  • mathematical physics
  • computational physics

Cite this

Johansson, T. ; Marin, L. / A procedure for the temperature reconstruction in corner domains from Cauchy data. In: Inverse Problems. 2007 ; Vol. 23, No. 1. pp. 357-372.
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Johansson, T & Marin, L 2007, 'A procedure for the temperature reconstruction in corner domains from Cauchy data', Inverse Problems, vol. 23, no. 1, pp. 357-372. https://doi.org/10.1088/0266-5611/23/1/020

A procedure for the temperature reconstruction in corner domains from Cauchy data. / Johansson, T.; Marin, L.

In: Inverse Problems, Vol. 23, No. 1, 17.01.2007, p. 357-372.

Research output: Contribution to journal › Article

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N2 - An iterative procedure is proposed for the reconstruction of a stationary temperature field from Cauchy data given on a part of the boundary of a bounded plane domain where the boundary is smooth except for a finite number of corner points. In each step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. Convergence is proved in a weighted L2-space. Numerical results are included which show that the procedure gives accurate and stable approximations in relatively few iterations.

AB - An iterative procedure is proposed for the reconstruction of a stationary temperature field from Cauchy data given on a part of the boundary of a bounded plane domain where the boundary is smooth except for a finite number of corner points. In each step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. Convergence is proved in a weighted L2-space. Numerical results are included which show that the procedure gives accurate and stable approximations in relatively few iterations.

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Johansson T, Marin L. A procedure for the temperature reconstruction in corner domains from Cauchy data. Inverse Problems. 2007 Jan 17;23(1):357-372. https://doi.org/10.1088/0266-5611/23/1/020

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