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A. Bespalov, D. Praetorius, M. Ruggeri:
"Two-level a posteriori error estimation for adaptive multilevel stochastic Galerkin FEM";
SIAM/ASA Journal on Uncertainty Quantification, 90 (2021), 3; S. 1184 - 1216.

The paper considers a class of parametric elliptic partial ifferential equations (PDEs), where the coefficients and the right-hand side function depend on infinitely many (uncertain) parameters. We introduce a two-level a posteriori estimator to control the energy error in multilevel stochastic Galerkin approximations for this class of PDE problems.We prove that the two-level estimator always provides a lower bound for the unknown approximation error, while the upper bound is equivalent to a saturation assumption.We propose and empirically compare three adaptive algorithms, where the structure
of the estimator is exploited to perform spatial refinement as well as parametric enrichment. The paper also discusses implementation aspects of computing multilevel stochastic Galerkin approximations.

adaptive methods, a posteriori error analysis, two-level error estimation, multilevel stochastic Galerkin methods, finite element methods, parametric PDEs

http://dx.doi.org/10.1137/20M1342586