Stanford 50: State of the Art and Future Directions of Computational Mathematics and Numerical Computing


  • March 30, 2007
  • 3:15 pm - 3:40 pm

The stochastic finite element method: Recent results and future directions

Howard Elman (University of Maryland)

Traditional methods of mathematical modeling depend on the assumption that components of models such as diffusion coefficients or boundary conditions are known. In practice, however, such quantities may not be known with certainty and instead they may be represented as random functions; that is, a random variable for each point in the physical domain.

An approach for performing computational studies of models of this type is the stochastic finite element method, which is a generalization of finite element discretization for deterministic problems designed to handle problems posed with uncertainty. We discuss the use of this methodology to model elliptic partial differential equations when some terms in the problem are not known with certainty, and we explore efficient solution algorithms based on multigrid to solve the large algebraic systems that arise from it.

In addition, we discuss computational issues that will affect the capability of this methodology to generate useful information about uncertain models.

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