2015/09/29 by Gabriel R. Barrenechea, Barrenechea, Gabriel R., Erik Burman +3 · 2 citations
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1509.08636
openalex publication_date 2015/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For the case of approximation of convection--diffusion equations using\npiecewise affine continuous finite elements a new edge-based nonlinear\ndiffusion operator is proposed that makes the scheme satisfy a discrete maximum\nprinciple. The diffusion operator is shown to be Lipschitz continuous and\nlinearity preserving. Using these properties we provide a full stability and\nerror analysis, which, in the diffusion dominated regime, shows existence,\nuniqueness and optimal convergence. Then the algebraic flux correction method\nis recalled and we show that the present method can be interpreted as an\nalgebraic flux correction method for a particular definition of the flux\nlimiters. The performance of the method is illustrated on some numerical test\ncases in two space dimensions.\n