## A stochastic modeling methodology based on weighted Wiener chaos and Malliavin calculus.

- Xiaoliang Wan, Boris Rozovskii, George Em Karniadakis
- Proceedings of the National Academy of Sciences…
- 2009

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7 Excerpts

- Published 2010

We consider parabolic SPDEs driven by purely spatial noise, and show the existence of solutions with random initial data and forcing terms. We perform error analysis for the semi-discrete stochastic finite element method applied to a class of equations with self-adjoint differential operators that are independent of time. The analysis employs the formal stochastic adjoint problem and the corresponding elliptic error estimates to obtain the optimal order of convergence (in space).

@inproceedings{Lee2010ASF,
title={A Stochastic Finite Element Method for Stochastic Parabolic Equations Driven by Purely Spatial Noise},
author={C. Y. Lee and Boris Rozovskii},
year={2010}
}