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Stochastic finite elements: Computational approaches to stochastic partial differential equations
Author(s) -
Matthies H.G.
Publication year - 2008
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200800095
Subject(s) - randomness , uncertainty quantification , monte carlo method , probabilistic logic , galerkin method , mathematical optimization , computer science , mathematics , perturbation (astronomy) , statistical physics , finite element method , machine learning , artificial intelligence , statistics , physics , quantum mechanics , thermodynamics
Uncertainty estimation arises at least implicitly in any kind of modelling of the real world, and it is desirable to actually quantify the uncertainty in probabilistic terms. Here the emphasis is on uncertain systems, where the randomness is assumed spatial. Traditional computational approaches usually use some form of perturbation or Monte Carlo simulation. This is contrasted here with more recent methods based on stochastic Galerkin approximations. Also some approaches to an adaptive uncertainty quantification are pointed out. \abstract{Uncertainty estimation arises at least implicitly in any kind of modelling of the real world, and it is desirable to actually quantify the uncertainty in probabilistic terms. Here the emphasis is on uncertain systems, where the randomness is assumed spatial. Traditional computational approaches usually use some form of perturbation or Monte Carlo simulation. This is contrasted here with more recent methods based on stochastic Galerkin approximations. Also some approaches to an adaptive uncertainty quantification are pointed out.}