Computable error estimators for the approximation of nonlinear problems by linearized models

In the modeling of nonlinear phenomena, a nonlinear model may often be replaced by a linear one, giving rise to a modeling or linearization error. This is in addition to the discretization error introduced when this linear model is solved, using, e.g., the finite element method. We investigate the a posteriori estimation of these errors for a general class of problems characterized by strongly monotone operators. Our results lead to the construction of computable upper estimators for the total error, with identifiable components from each of the these error sources. Several numerical tests evaluating the efficiency of our estimators are provided.