3 papers
math.NA2025
On positivity preservation of hybrid discontinuous Galerkin methods on hypergraphs
Petr Knobloch, Philip L. Lederer, Andreas Rupp
Hybrid finite element methods, particularly hybridized discontinuous Galerkin (HDG) methods, are efficient numerical schemes for discretizing the diffusion equation, which encompas…
math.NA2024
Well-balanced convex limiting for finite element discretizations of steady convection-diffusion-reaction equations
Petr Knobloch, Dmitri Kuzmin, Abhinav Jha
We address the numerical treatment of source terms in algebraic flux correction schemes for steady convection-diffusion-reaction (CDR) equations. The proposed algorithm constrains…
math.NA2023
Flux-corrected transport stabilization of an evolutionary cross-diffusion cancer invasion model
Shahin Heydari, Petr Knobloch, Thoma Wick
In the present work, we investigate a model of the invasion of healthy tissue by cancer cells which is described by a system of nonlinear PDEs consisting of a cross-diffusion-react…