Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Flux correction tools for finite elements
Journal of Computational Physics
SIAM Journal on Numerical Analysis
deal.II—A general-purpose object-oriented finite element library
ACM Transactions on Mathematical Software (TOMS)
A stabilized explicit Lagrange multiplier based domain decomposition method for parabolic problems
Journal of Computational Physics
Parallel Algorithms for Fluid-Structure Interaction Problems in Haemodynamics
SIAM Journal on Scientific Computing
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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 @q-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.