3 papers
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…
math.NA2022
An algebraically stabilized method for convection-diffusion-reaction problems with optimal experimental convergence rates on general meshes
Petr Knobloch
Algebraically stabilized finite element discretizations of scalar steady-state convection-diffusion-reaction equations often provide accurate approximate solutions satisfying the d…