Abstract
We present a novel adaptive algorithm implementing the stochastic Galerkin finite element method for numerical solution of elliptic PDE problems with correlated random data. The algorithm employs a hierarchical a posteriori error estimation strategy which also provides effective estimates of the error reduction for enhanced approximations. These error reduction indicators are used in the algorithm to perform a balanced adaptive refinement of spatial and parametric components of Galerkin approximations. The results of numerical tests demonstrating the efficiency of the algorithm for three representative PDEs with random coefficients are reported.
The software used for numerical experiments is available online.
The software used for numerical experiments is available online.
Original language | English |
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Pages (from-to) | 243–272 |
Journal | SIAM/ASA Journal on Uncertainty Quantification |
Volume | 6 |
Issue number | 1 |
Early online date | 6 Mar 2018 |
DOIs | |
Publication status | Published - 2018 |
Keywords
- stochastic Galerkin methods
- stochastic finite elements
- PDEs with random data
- adaptive methods
- a posteriori error estimation
- singularities
- parametric PDEs