Weighted overconstrained least-squares mixed finite elements for hyperelasticity

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)