2 papers
math.NA2025
A second-order-in-time scheme for the von Neumann equation with singular self-interaction and simulation of the onset of instability
Agissilaos Athanassoulis, Fotini Karakatsani, Irene Kyza
The von Neumann equation with delta self-interaction kernel serves as a statistical model for nonlinear waves, and it exhibits a bifurcation between stable and unstable regimes. In…
math.NA2015
Edge-based nonlinear diffusion for finite element approximations of convection-diffusion equations and its relation to algebraic flux-correction schemes
Gabriel R. Barrenechea, Erik Burman, Fotini Karakatsani
For the case of approximation of convection--diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that ma…