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Adaptive Stochastic Collocation on Sparse Grids
Author(s) -
Schieche Bettina
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210315
Subject(s) - collocation (remote sensing) , sparse grid , mathematics , partial differential equation , collocation method , stochastic differential equation , computer science , mathematical optimization , differential equation , ordinary differential equation , mathematical analysis , machine learning
We consider Partial Differential Equations (PDEs) with random parameters, solved by adaptive stochastic collocation. Our research studies common error indicators compared to adjoint based error estimates extended to the stochastic framework. We show that such estimates are able to detect the true error very accurately and suggest to replace the expensive adjoint problem by a reduced model. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)