Reliable and efficient equilibrated a posteriori finite element error control in elastoplasticity and elastoviscoplasticity with hardening

This paper establishes the reliability and efficiency of equilibrated a posteriori estimates for L2 stress error control of conforming displacement finite element approximations of incremental plasticity and viscoplasticity with hardening. Explicit expressions for upper bounds of the reliability constant that enters the guaranteed upper error bound illustrate its crucial dependence on the hardening material constants. Numerical experiments show that adaptive finite element solutions with marking strategy based on the max-refinement rule and local equilibrated error estimators lead to optimal empirical convergence rates.