Comparison of a mixed least-squares formulation using different approximation spaces

The main goal of the present work is the comparison of the performance of a least‐squares mixed finite element formulation where the solution variables (displacements and stresses) are interpolated using different approximation spaces. Basis for the formulation is a weak form resulting from the minimization of a least‐squares functional, compare e.g. [1]. As suitable functions for $H^1(\cal{B})$ standard interpolation polynomials of Lagrangian type are chosen. For the conforming discretization of the Sobolev space $H({\rm div}, \cal{B})$ vector‐valued Raviart‐Thomas interpolation functions, see also [2], are used. The resulting elements are named as PmPk and RTmPk. Here m (stresses) and k (displacements) denote the approximation order of the particular interpolation function. For the comparison we consider a two‐dimensional cantilever beam under plain strain conditions and small strain assumptions. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)