T-IFISS

Efficient adaptive algorithms for elliptic PDEs with random data. 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.


References in zbMATH (referenced in 13 articles , 2 standard articles )

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  1. Cao, Xiaoting; Zhang, Xiaohua; Shi, Xiaotao: An adaptive variational multiscale element free Galerkin method based on the residual-based a posteriori error estimators for convection-diffusion-reaction problems (2022)
  2. Bespalov, Alex; Praetorius, Dirk; Ruggeri, Michele: Two-level a posteriori error estimation for adaptive multilevel stochastic Galerkin finite element method (2021)
  3. Bespalov, Alex; Rocchi, Leonardo; Silvester, David: T-IFISS: a toolbox for adaptive FEM computation (2021)
  4. Khan, Arbaz; Bespalov, Alex; Powell, Catherine E.; Silvester, David J.: Robust a posteriori error estimation for parameter-dependent linear elasticity equations (2021)
  5. Zhang, Xiaohua; Hu, Zhicheng; Wang, Min: An adaptive interpolation element free Galerkin method based on a posteriori error estimation of FEM for Poisson equation (2021)
  6. Bespalov, Alex; Xu, Feng: A posteriori error estimation and adaptivity in stochastic Galerkin FEM for parametric elliptic PDEs: beyond the affine case (2020)
  7. Lang, J.; Scheichl, R.; Silvester, D.: A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data (2020)
  8. Liu, Jun; Wu, Shu-Lin: A fast block (\alpha)-circulant preconditoner for all-at-once systems from wave equations (2020)
  9. Bespalov, Alex; Praetorius, Dirk; Rocchi, Leonardo; Ruggeri, Michele: Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs (2019)
  10. Bespalov, Alex; Praetorius, Dirk; Rocchi, Leonardo; Ruggeri, Michele: Convergence of adaptive stochastic Galerkin FEM (2019)
  11. Crowder, Adam J.; Powell, Catherine E.; Bespalov, Alex: Efficient adaptive multilevel stochastic Galerkin approximation using implicit a posteriori error estimation (2019)
  12. Bespalov, Alex; Rocchi, Leonardo: Efficient adaptive algorithms for elliptic PDEs with random data (2018)
  13. Crowder, Adam J.; Powell, Catherine E.: CBS constants & their role in error estimation for stochastic Galerkin finite element methods (2018)