Robust a posteriori error estimation for the nonconforming Fortin-Soulie finite element approximation

We obtain a computable a posteriori error bound on the broken energy norm of the error in the Fortin–Soulie finite element approximation of a linear second order elliptic problem with variable permeability. This bound is shown to be efficient in the sense that it also provides a lower bound for the broken energy norm of the error up to a constant and higher order data oscillation terms. The estimator is completely free of unknown constants and provides a guaranteed numerical bound on the error.