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- Title
Weighted overconstrained least-squares mixed finite elements for hyperelasticity.
- Authors
Schwarz, Alexander; Steeger, Karl; Schröder, Jörg
- Abstract
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)
- Subjects
FINITE element method; LEAST squares; APPROXIMATION theory; NONLINEAR elastic fracture; BENDING (Metalwork); GALERKIN methods
- Publication
PAMM: Proceedings in Applied Mathematics & Mechanics, 2015, Vol 15, Issue 1, p227
- ISSN
1617-7061
- Publication type
Article
- DOI
10.1002/pamm.201510104