Gradients and the performance of numerical models

Abstract

Given a differentiable function, the properties of the gradient vector of f are well known for each . It will be examined a non trivial problem in the domain of the Applied Mathematics in which the role of the gradient of a certain functional in the definition of the differential of this functional is essential to the development of an efficient algorithm in order to obtain one configuration of the evolutionary system, when we have a numerical model of the system dynamics and a space-time distributed set of observations of the same system, useful in the prediction of the future behavior of the system under study, and which can also be used as a powerful method for the analysis of the numerical model performance. Keywords: 4D variational data assimilation, control theory, applied mathematics, pollutant spillage detection.