Error Indicator For Mixed Finite Elements

Abstract

The main objective of this paper is to propose an “a posteriori”error indicator
and a finite element adaptive strategy for the Reissner-Hellinger thermo–elasticity
formulation. The paper presents triangular finite elements with quadratic and continuous
displacements interpolation and discontinuous stress interpolation. Two different interpolations
for the stress field are considered. In plane stress condition, total stress is linearly
interpolated. Likewise, the deviatoric stress is regarded as linear for plane strain and under
symmetry of revolution conditions but the mean stress is considered to be constant in
each element. These mixed elements are appropriated for facing the locking phenomena
when incompressibility is presented. The proposed error indicator is based on second-order
derivatives of the Mises equivalent stress and mean stress associated with a recovered stress
field. That is, gradients and/or Hessians of the stress solution, obtained on a given mesh,
are smoothed and then used in the error estimation. The error indicator is related with the
maximum eigenvalue of such Hessians. Some numerical examples are presented in order
to show the viability of this adaptive mesh refinement and to compare its performance with
the error estimates found in literature.