A posteriori error estimates and maximal regularity for approximations of fully nonlinear parabolic problems in Banach spaces

A posteriori error estimates are provided for discretizations in time of abstract nonlinear parabolic problems u′ = F(u), by the backward Euler method in the maximal regularity framework of Banach spaces. The estimates are of conditional type, i.e., are valid under assumptions on the approximate solution, and the proofs are based on appropriate fixed point arguments. Work partially supported by Grant HPMD-CT-200100121, Institute of Applied and Computational Mathematics, FORTH, 71110 Heraklion-Crete, Greece, by a Spain–Greece Research Collaboration grant jointly funded by the Ministry of Education and Science, Spain, and the General Secretariat of Research and Technology, Greece and a Pytrhagoras–EPEAEK II grant.