An a posteriori error estimate for the generalized finite element method for transient heat diffusion problems

Summary We propose the study of a posteriori error estimates for time‐dependent generalized finite element simulations of heat transfer problems. A residual estimate is shown to provide reliable and practically useful upper bounds for the numerical errors, independent of the heuristically chosen enr...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2017-06, Vol.110 (12), p.1103-1118
Main Authors: Iqbal, Muhammad, Gimperlein, Heiko, Mohamed, M. Shadi, Laghrouche, Omar
Format: Article
Language:English
Subjects:
adaptivity
Enrichment
Error analysis
error estimation
Exact solutions
extended finite element method
Finite element method
finite element methods
generalized finite element method
Mathematical analysis
thermal effects
Time dependence
Upper bounds
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Summary:Summary We propose the study of a posteriori error estimates for time‐dependent generalized finite element simulations of heat transfer problems. A residual estimate is shown to provide reliable and practically useful upper bounds for the numerical errors, independent of the heuristically chosen enrichment functions. Two sets of numerical experiments are presented. First, the error estimate is shown to capture the decrease in the error as the number of enrichment functions is increased or the time discretization refined. Second, the estimate is used to predict the behaviour of the error where no exact solution is available. It also reflects the errors incurred in the poorly conditioned systems typically encountered in generalized finite element methods. Finally, we study local error indicators in individual time steps and elements of the mesh. This creates a basis towards the adaptive selection and refinement of the enrichment functions. Copyright © 2016 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.5440