Error control for nonlinear evolution equations

C.R. Acad. Sci. Paris, Serie I, 326 (1998), 1437-1442.

Ricardo H. Nochetto
Department of Mathematics
University of Maryland, College Park
College Park, MD 20742, USA

Giuseppe Savare
Istituto di Analisi Numerica del C.N.R.
27100 Pavia, Italy

Claudio Verdi
Dipartimento di Matematica
Universita di Milano
Milano, 20133, Italy


We derive 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-boundedy. 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 both order and regularity.