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Weighted overconstrained least‐squares mixed finite elements for hyperelasticity
Author(s) -
Schwarz Alexander,
Steeger Karl,
Schröder Jörg
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510104
Subject(s) - finite element method , mathematics , robustness (evolution) , galerkin method , nonlinear system , hyperelastic material , interpolation (computer graphics) , least squares function approximation , constraint (computer aided design) , moving least squares , mathematical analysis , computer science , geometry , structural engineering , engineering , animation , chemistry , physics , computer graphics (images) , statistics , quantum mechanics , estimator , gene , biochemistry
The present contribution aims to improve the least‐squares finite element method (LSFEM) with respect to the approximation quality in hyperelasticity. We consider a geometrically nonlinear elastic setup and here especially bending dominated problems. Compared with other variational approaches as for example the Galerkin method, the main drawback of least‐squares formulations is the unsatisfying approximation quality in terms of accuracy and robustness of especially lower‐order elements, see e.g. SCHWARZ ET AL. [1]. In order to circumvent these problems, we introduce an overconstrained first‐order stress‐displacement system with suited weights. For the interpolation of the unknowns standard polynomials for the displacements and vector‐valued Raviart‐Thomas functions for the approximation of the stresses are used. Finally, a numerical example is presented in order to show the improvement of performance and accuracy. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)