A procedure for the reconstruction of a stochastic stationary temperature field

Bjorn Johansson

Research output: Contribution to journalArticle


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
Issue number4
Early online date17 Nov 2007
Publication statusPublished - 17 Nov 2008


  • finite element
  • Karhunen-Loeve expansion
  • ill posed
  • stochastic elliptic equation


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