Error control of nonlinear evolution equations

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