ExtendableASGFEM

This package implements the stochastic Galerkin finite element method for certain two dimensional model problems involving KLE of stochastic coefficients. The rather huge systems have a tensorized structure and are solved by iterative solvers. A posteriori error estimators steer the spatial and stochastic refinement.

The spatial discretization is based on the finite element package ExtendableFEM.jl/ExtendableFEMBase.jl

References

• [1] "Adaptive stochastic Galerkin FEM"
  M. Eigel, C.J. Gittelson, C. Schwab, E. Zander
  CMAME 270, 1 (2014), 247–269
  >Journal-Link< >Preprint-Link<
• [2] "A posteriori error control for stochastic Galerkin FEM with high-dimensional random parametric PDEs",
  M. Eigel, C. Merdon
  to be published in: Error Control, Adaptive Discretizations, and Applications, Part 3, Academic Press
  >Preprint-Link<
• [3] "Local equilibration error estimators for guaranteed error control in adaptive higher-order stochastic Galerkin finite element methods"
  M. Eigel and C. Merdon
  SIAM/ASA J. Uncertainty Quantification 4(1) (2016), 1372–1397"
  >Journal-Link< >Preprint-Link<