Stochastic Galerkin Matrices

We investigate the structural, spectral, and sparsity properties of Stochastic Galerkin matrices as they arise in the discretization of linear differential equations with random coefficient functions. These matrices are characterized as the Galerkin representation of polynomial multiplication operators. In particular, it is shown that the global Galerkin matrix associated with complete polynomials cannot be diagonalized in the stochastically linear case. Key words. stochastic Galerkin method, stochastic finite elements, orthogonal polynomials AMS subject classifications. 65N30, 65C30, 15A18 DOI. 10.1137/080742282

• Type: Journal
• Year: 2010
• Where: SIAMMAX
• Authors: Oliver G. Ernst, Elisabeth Ullmann
• Keywords: Global Galerkin Matrix, SIAMMAX 2010, Stochastic Galerkin, Stochastic Galerkin Method