This paper presents an adaptive numerical analysis for primal elastoplasticity with hardening. The authors analyze the convergence of the primal formulation of elastoplasticity, which models material behavior using strain as the primary variable. They show that the primal formulation leads to linear convergence in the spatial discretization, which is supported by both theoretical and numerical results. The analysis is based on a posteriori error estimates that justify an adaptive mesh-refining algorithm. The authors also compare the primal and dual formulations, showing that the primal formulation is equally accurate but more favorable for higher-order schemes. The paper includes numerical examples that demonstrate the effectiveness of the adaptive mesh-refining algorithm in improving convergence and computational efficiency. The analysis is conducted for both isotropic and kinematic hardening cases, and the results are validated through various examples. The authors also discuss the use of a posteriori error estimates in the context of viscoplasticity and plasticity with hardening, and they highlight the importance of adaptive mesh-refining for efficient numerical treatment of elastoplastic problems. The paper concludes with a discussion of the implications of the results for future research in this area.This paper presents an adaptive numerical analysis for primal elastoplasticity with hardening. The authors analyze the convergence of the primal formulation of elastoplasticity, which models material behavior using strain as the primary variable. They show that the primal formulation leads to linear convergence in the spatial discretization, which is supported by both theoretical and numerical results. The analysis is based on a posteriori error estimates that justify an adaptive mesh-refining algorithm. The authors also compare the primal and dual formulations, showing that the primal formulation is equally accurate but more favorable for higher-order schemes. The paper includes numerical examples that demonstrate the effectiveness of the adaptive mesh-refining algorithm in improving convergence and computational efficiency. The analysis is conducted for both isotropic and kinematic hardening cases, and the results are validated through various examples. The authors also discuss the use of a posteriori error estimates in the context of viscoplasticity and plasticity with hardening, and they highlight the importance of adaptive mesh-refining for efficient numerical treatment of elastoplastic problems. The paper concludes with a discussion of the implications of the results for future research in this area.