41 citations · 176 across the 16 of their papers we have counts for
19 papers
Weighted Essentially Non-Oscillatory stochastic Galerkin approximation for hyperbolic conservation laws
Louisa Schlachter, Florian Schneider, Oliver Kolb
In this paper we extensively study the stochastic Galerkin scheme for uncertain systems of conservation laws, which appears to produce oscillations already for a simple example of…
The second-order formulation of the equations with Marshak boundary conditions
Matthias Andres, Florian Schneider
We consider a reformulation of the classical method with Marshak boundary conditions for the approximation of the monoenergetic stationary linear transport equation as a syst…
First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: realizability-preserving splitting scheme and numerical analysis
Florian Schneider, Tobias Leibner
We derive a second-order realizability-preserving scheme for moment models for linear kinetic equations. We apply this scheme to the first-order continuous and discontinuous models…
First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: model derivation and realizability theory
Florian Schneider, Tobias Leibner
We provide two new classes of moment models for linear kinetic equations in slab and three-dimensional geometry. They are based on classical finite elements and low-order discontin…
A hyperbolicity-preserving discontinuous stochastic Galerkin scheme for uncertain hyperbolic systems of equations
Jakob Dürrwächter, Thomas Kuhn, Fabian Meyer +2
Intrusive Uncertainty Quantification methods such as stochastic Galerkin are gaining popularity, whereas the classical stochastic Galerkin approach is not ensured to preserve hyper…
Higher-order models for glioma invasion: from a two-scale description to effective equations for mass density and momentum
Gregor Corbin, Alexander Hunt, Florian Schneider +2
Starting from a two-scale description involving receptor binding dynamics and a kinetic transport equation for the evolution of the cell density function under velocity reorientati…
A hyperbolicity-preserving stochastic Galerkin approximation for uncertain hyperbolic systems of equations
Louisa Schlachter, Florian Schneider
Uncertainty Quantification through stochastic spectral methods is rising in popularity. We derive a modification of the classical stochastic Galerkin method, that ensures the hyper…
Second-order mixed-moment model with differentiable ansatz function in slab geometry
Florian Schneider
We study differentiable mixed-moment models (full zeroth and first moment, half higher moments) for a Fokker-Planck equation in one space dimension. Mixed-moment minimum-entropy mo…
A Comparative Study of Limiting Strategies in Discontinuous Galerkin Schemes for the Model of Radiation Transport
Prince Chidyagwai, Martin Frank, Florian Schneider +1
The minimum entropy moment system is a system of hyperbolic balance laws that approximates the radiation transport equation, and has many desirable properties. Among them are…
A numerical comparison of the method of moments for the population balance equation
Laura Müller, Axel Klar, Florian Schneider
We investigate the application of the method of moments approach for the one-dimensional population balance equation. We consider different types of moment closures, namely polynom…
Implicit-explicit, realizability-preserving first-order scheme for moment models with Lipschitz-continuous source terms
Florian Schneider
We derive an implicit-explicit (IMEX), realizability-preserving first-order scheme for moment models with Lipschitz-continuous source terms. In contrast to fully-explicit schemes t…
Kershaw closures for linear transport equations in slab geometry II: high-order realizability-preserving discontinuous-Galerkin schemes
Florian Schneider
This paper provides a generalization of the realizability-preserving discontinuous-Galerkin scheme for quadrature-based minimum-entropy models to full-moment models of arbitrary or…
Partial-moment minimum-entropy models for kinetic chemotaxis equations in one and two dimensions
Juliane Ritter, Axel Klar, Florian Schneider
The aim of this work is to investigate the application of partial moment approximations to kinetic chemotaxis equations in one and two spatial dimensions. Starting with a kinetic e…
Kershaw closures for linear transport equations in slab geometry I: model derivation
Florian Schneider
This paper provides a new class of moment models for linear kinetic equations in slab geometry. These models can be evaluated cheaply while preserving the important realizability p…
First-order quarter- and mixed-moment realizability theory and Kershaw closures for a Fokker-Planck equation in two space dimensions
Florian Schneider, Jochen Kall, Andreas Roth
Mixed-moment models, introduced before for one space dimension, are a modification of the method of moments applied to a (linear) kinetic equation, by choosing mixtures of differen…
A realizability-preserving high-order kinetic scheme using WENO reconstruction for entropy-based moment closures of linear kinetic equations in slab geometry
Florian Schneider, Graham Alldredge, Jochen Kall
We develop a high-order kinetic scheme for entropy-based moment models of a one-dimensional linear kinetic equation in slab geometry. High-order spatial reconstructions are achieve…
A realizability-preserving discontinuous Galerkin scheme for entropy-based moment closures for linear kinetic equations in one space dimension
Graham Alldredge, Florian Schneider
We implement a high-order numerical scheme for the entropy-based moment closure, the so-called M model, for linear kinetic equations in slab geometry. A discontinuous Galerkin…
Higher order mixed moment approximations for the Fokker-Planck equation in one space dimension
Florian Schneider, Graham Alldredge, Martin Frank +1
We study mixed-moment models (full zeroth moment, half higher moments) for a Fokker-Planck equation in one space dimension. Mixed-moment minimum-entropy models are known to overcom…
The Semi-Classical Limit of an Optimal Design Problem for the Stationary Quantum Drift-Diffusion Model
René Pinnau, Sebastian Rau, Florian Schneider +1
We consider an optimal semiconductor design problem for the quantum drift diffusion (QDD) model in the semiclassical limit. The design question is formulated as a PDE constrained o…