9 citations · 22 across the 8 of their papers we have counts for
9 papers
Application of Machine Learning to the Computation of Parameters in the SUPG Method for Unstructured and Anisotropic Meshes
Petr Knobloch, Manoj Prakash
Solution of convection-dominated problems using stabilized methods often requires to specify stabilization parameters whose optimal choice is not known but which considerably influ…
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…
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…
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…
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…
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…
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…
On algebraically stabilized schemes for convection-diffusion-reaction problems
Volker John, Petr Knobloch
An abstract framework is developed that enables the analysis of algebraically stabilized discretizations in a unified way. This framework is applied to a discretization of this kin…
Adaptive Grids in the Context of Algebraic Stabilizations for Convection-Diffusion-Reaction Equations
Abhinav Jha, Volker John, Petr Knobloch
Three algebraically stabilized finite element schemes for discretizing convection-diffusion-reaction equations are studied on adaptively refined grids. These schemes are the algebr…