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

Julia Vuong, Bernd Simeon
2014 Journal of Computational and Applied Mathematics  
An extension of the finite element method-flux corrected transport stabilization (FEM-FCT) for hyperbolic problems in the context of partial differentialalgebraic equations (PDAEs) is proposed. Given a local extremum diminishing property of the spatial discretization, the positivity preservation of the one-step θ−scheme when applied to the time integration of the resulting differentialalgebraic equation (DAE) is shown, under a mild restriction on the time stepsize. As crucial tool in the
more » ... s, the Drazin inverse and the corresponding Drazin ODE are explicitly derived. Numerical results are presented for nonconstant and time-dependent boundary conditions in one space dimension and for a two-dimensional advection problem where the advection proceeds skew to the mesh.
doi:10.1016/j.cam.2013.09.070 fatcat:u2blj7m6jzch7ixohqi6qgiyte