Error control of nonlinear evolution equations

We derive novel a posteriori error estimates for backward Euler approximations of evo- lution inequalities in Hilbert spaces. The underlying nonlinear (multivalued) monotone operator is subdifferential, or more generally angle-bounded. The estimates depend solely on the discrete so- lution data, impose no constraints between consecutive time-steps, exhibit explicit stability factors, and are optimal with respect to both order and regularity.