Tikhonov-type regularization and the finite element method applied to point source estimation in the atmosphere

Abstract This work is concerned with the source identification problem in air pollution modeling. The forward problem is described by an advection-diffusion equation with physically realistic coefficients. It is solved by the combination of adaptive meshes and a stabilized finite element method. The source is estimated by Tikhonov-type regularization with a composite misfit function and an entropic penalty term. The composite misfit is given by the convex combination of l 1 and l 2 norms of the discrepancy between observed and predicted concentrations. Morozov's discrepancy principle is applied to simultaneously choose the regularization and the misfit combination parameters. Numerical experiments using Copenhagen field data is used to validate numerically the proposed methodology.