A POSTERIORI ERROR ANALYSIS OF STOCHASTIC DIFFERENTIAL EQUATIONS USING POLYNOMIAL CHAOS EXPANSIONS

作者：Butler T^*; Dawson C; Wildey T

来源：SIAM Journal on Scientific Computing, 2011, 33(3): 1267-1291.

DOI：10.1137/100795760

• a posteriori error analysis
• adjoint problem
• polynomial chaos
• stochastic spectral methods

We develop computable a posteriori error estimates for linear functionals of a solution to a general nonlinear stochastic differential equation with random model/source parameters. These error estimates are based on a variational analysis applied to stochastic Galerkin methods for forward and adjoint problems. The result is a representation for the error estimate as a polynomial in the random model/source parameter. The advantage of this method is that we use polynomial chaos representations for the forward and adjoint systems to cheaply produce error estimates by simple evaluation of a polynomial. By comparison, the typical method of producing such estimates requires repeated forward/adjoint solves for each new choice of random parameter. We present numerical examples showing that there is excellent agreement between these methods.

• 出版日期2011