A high order positivity preserving DG method for coagulation-fragmentation equations

2017/10/03 by Liu, Hailiang, Gröpler, Robin, Warnecke, Gerald · 1 citation
#35L65 #65M12 #65M60 #65R20 #82C22 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1710.00964

Abstract

We design, analyze and numerically validate a novel discontinuous Galerkin method for solving the coagulation-fragmentation equations. The DG discretization is applied to the conservative form of the model, with flux terms evaluated by Gaussian quadrature with Q=k+1 quadrature points for polynomials of degree k. The positivity of the numerical solution is enforced through a simple scaling limiter based on positive cell averages. The positivity of cell averages is propagated by the time discretization provided a proper time step restriction is imposed.

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