Finite element approximation of penalized elastoplastic torsion problem with nonconstant source term

This study is concerned with the finite element approximation of the elastoplastic torsion problem. We focus on the case of a nonconstant source term, which cannot be easily recast into an obstacle problem as can be done in the case of a constant source term. We present a simple formulation that penalizes the constraint directly on the gradient norm of the solution. We study its well-posedness, derive error estimates and present numerical results to illustrate the theory.