Using the Generalized Collage Theorem for Estimating Unknown Parameters in Perturbed Mixed Variational Equations

The use of mixed variational formulations in mathematical modeling, as well as their numerical implementation, are well known areas of mathematical and numerical analysis that have been well-investigated in the literature. In this paper, we study a mixed variational problem subject to perturbations, where the noise term is modelled by means of a bilinear form that has to be understood to be "small" in some sense. For this new formulation we provide a result that guarantees existence and uniqueness of the solution. We introduce the corresponding Galerkin method and study its convergence. We also analyze the associated inverse problem and we show how to solve it by means of an extension of the Generalized Collage Theorem which extends previous results by the same authors. Numerical examples show how the method works in a practical context.