Higher-order sensitivity of heat conduction problems to random data using the spectral stochastic finite element method

The spectral formulation of the stochastic finite element method is applied to the problem of heat conduction in a random medium. Specifically, the conductivity of the medium, as well as its heat capacity are treated as uncorrelated random processes with spatial random fluctuations, This paper introduces the basic concepts of the spectral stochastic finite element method using a simple one-dimensional heat conduction examples. The implementation of the method is demonstrated for both Gaussian and log-normal material properties, Moreover, the case of the material properties being modeled as random variables is presented as a simple digression of the formulation for the stochastic process case. Both Gaussian and log-normal models for the material properties are treated.