### Abstract

Original language | English |
---|---|

Pages (from-to) | 641-650 |

Number of pages | 10 |

Journal | IMA Journal of Applied Mathematics |

Volume | 73 |

Issue number | 4 |

Early online date | 14 Dec 2007 |

DOIs | |

Publication status | Published - 2008 |

### Fingerprint

### Keywords

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

### Cite this

*IMA Journal of Applied Mathematics*,

*73*(4), 641-650. https://doi.org/10.1093/imamat/hxm057

}

*IMA Journal of Applied Mathematics*, vol. 73, no. 4, pp. 641-650. https://doi.org/10.1093/imamat/hxm057

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - A procedure for the reconstruction of a stochastic stationary temperature field

AU - Johansson, B. Tomas

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - finite element

KW - ill posed

KW - Karhunen–Loève expansion

KW - stochastic elliptic equation

UR - http://imamat.oxfordjournals.org/content/73/4/641.abstract?sid=840336cd-4da6-4b3d-b5e0-1126affc0d73

U2 - 10.1093/imamat/hxm057

DO - 10.1093/imamat/hxm057

M3 - Article

VL - 73

SP - 641

EP - 650

JO - IMA Journal of Applied Mathematics

JF - IMA Journal of Applied Mathematics

SN - 0272-4960

IS - 4

ER -