Talks and Poster Presentations (without Proceedings-Entry):

A. Bespalov, D. Praetorius, M. Ruggeri, L. Rocchi:
"Adaptive stochastic Galerkin FEM for parametric PDEs";
Talk: 14th Austrian Numerical Analysis Day, Klagenfurt; 2018-05-03 - 2018-05-04.

English abstract:
Parametric partial differential equations (PDEs) arise in several contexts such as inverse and optimization problems, uncertainty quantification, and reduced basis approximations. In such PDEs, the differential operators might depend on large, possibly infinite, sets of parameters, so that naive applications of standard numerical methods often lead to the so-called `curse of dimensionality'. In this talk, we present an adaptive stochastic Galerkin FEM for parametric elliptic boundary value problems. The adaptive algorithm employs an a posteriori error estimator, which can be decomposed into a two-level estimator in the physical domain and a hierarchical estimator in the parameter domain. This structure of the estimated error is exploited by the algorithm to perform a balanced adaptive refinement of the spatial and parametric discretizations.

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