ExtendableASGFEM

This package provides an implementation of the stochastic Galerkin finite element method (SGFEM) for selected two-dimensional model problems involving Karhunen-Loève expansions (KLE) of stochastic coefficients. The resulting large-scale systems exhibit a tensorized structure and are efficiently solved using iterative solvers. Adaptive a posteriori error estimators guide both spatial and stochastic refinement to ensure accuracy and efficiency.

Spatial discretization is performed using the finite element packages ExtendableFEM.jl and ExtendableFEMBase.jl.

Example Script

A script for running adaptive SGFEM experiments is provided in scripts/poisson.jl. It supports:

• Poisson problem with linear coefficient
• Log-transformed Poisson problem with exponential coefficient
• Dual formulation of the log-transformed problem (WIP)

The script handles both spatial and stochastic adaptivity, and includes tools for result visualization and error analysis. For a detailed description of all available parameters and usage instructions, see Script Documentation.

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 appear 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