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

rhn@math.umd.edu

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

savare@dragon.ian.pv.cnr.it

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

verdi@paola.mat.unimi.it

Abstract

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.