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Duality‐based adaptive model reduction for one‐way coupled thermoelastic problems
Author(s) -
Jakobsson Håkan,
Bengzon Fredrik,
Larson Mats G.
Publication year - 2012
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4273
Subject(s) - thermoelastic damping , finite element method , discretization , duality (order theory) , mathematics , reduction (mathematics) , a priori and a posteriori , mixed finite element method , extended finite element method , mathematical analysis , geometry , thermal , physics , structural engineering , discrete mathematics , engineering , philosophy , epistemology , meteorology
SUMMARY In this paper, we derive a discrete a posteriori error estimate for a thermoelastic model problem discretized using a reduced finite element method. The problem is one‐way coupled in the sense that heat transfer affects elastic deformation but not vice versa. A reduced model is constructed using component mode synthesis in each of the heat transfer and linear elastic finite element solvers. The error estimate bounds the difference between the reduced and the standard finite element solution in terms of discrete residuals and corresponding dual weights. A main feature with the estimate is that it automatically gives a quantitative measure of the propagation of error between the solvers with respect to a certain computational goal. The analytical results are accompanied by a numerical example. Copyright © 2012 John Wiley & Sons, Ltd.