Approximating Infinity-Dimensional Stochastic Darcy's Equations without Uniform Ellipticity

@article{Galvis2009ApproximatingIS,
  title={Approximating Infinity-Dimensional Stochastic Darcy's Equations without Uniform Ellipticity},
  author={Juan Galvis and Marcus Sarkis},
  journal={SIAM J. Numerical Analysis},
  year={2009},
  volume={47},
  pages={3624-3651}
}
We consider a stochastic Darcy’s pressure equation whose coefficient is generated by a white noise process on a Hilbert space employing the ordinary (rather than the Wick) product. A weak form of this equation involves different spaces for the solution and test functions and we establish a continuous inf-sup condition and well-posedness of the problem. We generalize the numerical approximations proposed in Benth and Theting [Stochastic Anal. Appl., 20 (2002), pp. 1191–1223] for Wick stochastic… CONTINUE READING

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