H(div) preconditioning for a mixed finite element formulation of the diffusion problem with random data

@article{Elman2010HdivPF,
  title={H(div) preconditioning for a mixed finite element formulation of the diffusion problem with random data},
  author={Howard C. Elman and Darran G. Furnival and Catherine Elizabeth Powell},
  journal={Math. Comput.},
  year={2010},
  volume={79},
  pages={733-760}
}
We study H(div) preconditioning for the saddle-point systems that arise in a stochastic Galerkin mixed formulation of the steady-state diffusion problem with random data. The key ingredient is a multigrid V-cycle for an H(div) operator with random weight function acting on a certain tensor product space of random fields with finite variance. We build on the ArnoldFalk-Winther multigrid algorithm presented in 1997 by varying the spatial discretization from grid to grid whilst keeping the… CONTINUE READING