A procedure for the reconstruction of a stochastic stationary temperature field

B. Tomas Johansson

Research output: Contribution to journalArticle

Abstract

An iterative procedure is proposed for the reconstruction of a temperature field from a linear stationary heat equation with stochastic coefficients, and stochastic Cauchy data given on a part of the boundary of a bounded domain. In each step, a series of mixed well-posed boundary-value problems are solved for the stochastic heat operator and its adjoint. Well-posedness of these problems is shown to hold and convergence in the mean of the procedure is proved. A discretized version of this procedure, based on a Monte Carlo Galerkin finite-element method, suitable for numerical implementation is discussed. It is demonstrated that the solution to the discretized problem converges to the continuous as the mesh size tends to zero.
Original languageEnglish
Pages (from-to)641-650
Number of pages10
JournalIMA Journal of Applied Mathematics
Volume73
Issue number4
Early online date14 Dec 2007
DOIs
Publication statusPublished - 2008

Fingerprint

Temperature Field
Temperature distribution
Boundary value problems
Galerkin Finite Element Method
Iterative Procedure
Finite element method
Well-posedness
Heat Equation
Cauchy
Bounded Domain
Heat
Boundary Value Problem
Mesh
Tend
Converge
Series
Zero
Coefficient
Operator
Hot Temperature

Keywords

  • finite element
  • ill posed
  • Karhunen–Loève expansion
  • stochastic elliptic equation

Cite this

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A procedure for the reconstruction of a stochastic stationary temperature field. / Johansson, B. Tomas.

In: IMA Journal of Applied Mathematics, Vol. 73, No. 4, 2008, p. 641-650.

Research output: Contribution to journalArticle

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