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Towards adaptive discontinuous Petrov‐Galerkin methods
Author(s) -
Bringmann P.,
Carstensen C.,
Gallistl D.,
Hellwig F.,
Peterseim D.,
Puttkammer S.,
Rabus H.,
Storn J.
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610359
Subject(s) - petrov–galerkin method , discontinuous galerkin method , mathematics , elasticity (physics) , residual , stability (learning theory) , poisson distribution , linear elasticity , mathematical optimization , mathematical analysis , finite element method , computer science , algorithm , physics , statistics , machine learning , thermodynamics
The discontinuous Petrov‐Galerkin (dPG) method is a minimum residual method with broken test functions for instant stability. The methodology is written in an abstract framework with product spaces. It is applied to the Poisson model problem, the Stokes equation, and linear elasticity with low‐order discretizations. The computable residuum leads to guaranteed error bounds and motivates adaptive refinements. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)