2016-01-142016-01-142007Chacón Rebollo, T., Gómez Mármol, M.M. y Narbona-Reina, G. (2007). Numerical analysis of the PSI solution of advection–diffusion problems through a Petrov–Galerkin formulation. Mathematical Models and Methods in Applied Sciences, 17 (11), 1905-1936.0218-2025http://hdl.handle.net/11441/32516We consider a system composed by two immiscible fluids in two-dimensional space that can be modelized by a bilayer Shallow Water equations with extra friction terms and capillary effects. We give an existence theorem of global weak solutions in a periodic domain.In this paper we introduce an analysis technique for the solution of the steady advection– diffusion equation by the PSI (Positive Streamwise Implicit) method. We formulate this approximation as a nonlinear finite element Petrov–Galerkin scheme, and use tools of functional analysis to perform a convergence, error and maximum principle analysis. We prove that the scheme is first-order accurate in H1 norm, and well-balanced up to second order for convection-dominated flows. We give some numerical evidence that the scheme is only first-order accurate in L2 norm. Our analysis also holds for other nonlinear Fluctuation Splitting schemes that can be built from first-order monotone schemes by the Abgrall and Mezine’s technique.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Fluctuation splitting schemesFinite elementconvection–diffusion probleminfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1142/S0218202507002510https://idus.us.es/xmlui/handle/11441/32516