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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…
math.NA2022★ 9 cited
Global existence of classical solutions and numerical simulations of a cancer invasion model
Mario Fuest, Shahin Heydari, Petr Knobloch +2
In this paper, we study a cancer invasion model both theoretically and numerically. The model is a nonstationary, nonlinear system of three coupled partial differential equations m…
math.NA2022★ 6 cited
Finite element methods respecting the discrete maximum principle for convection-diffusion equations
Gabriel R. Barrenechea, Volker John, Petr Knobloch
Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solution of these equations satisfy under certain conditions m…