Resumen de On finite element method-flux corrected transport stabilization for advection-diffusion problems in a partial differential-algebraic framework

Julia Vuong, Bernd Simeon

• An extension of the finite element method�flux corrected transport stabilization for hyperbolic problems in the context of partial differential�algebraic equations is proposed.

  Given a local extremum diminishing property of the spatial discretization, the positivity preservation of the one-step è-scheme when applied to the time integration of the resulting differential�algebraic equation is shown, under a mild restriction on the time step size. As a crucial tool in the analysis, the Drazin inverse and the corresponding Drazin ordinary differential equation are explicitly derived. Numerical results are presented for non-constant and time-dependent boundary conditions in one space dimension and for a two-dimensional advection problem with a sinusoidal inflow boundary condition and the advection proceeding skew to the mesh.