In this note, a priori error estimates in the energy norm are derived for a finite element discretisation of the
torsion problem. Studying suboptimal results of a direct approach following
Glowinski, it turns out to be convenient to treat this problem by a Lagrangian
formalism. The approach offers several alternatives for the numerical
analysis of variational inequalities.
We mention the iterative solution process of the discrete problems
and focus on alternatives for a priori error analysis. Furthermore, we derive an a posteriori error bound for the
discretisation error measured in the energy norm.