12 papers
Stability of the Active Flux Method in the Framework of Summation-by-Parts Operators
Wasilij Barsukow, Christian Klingenberg, Lisa Lechner +3
The Active Flux method is a numerical method for conservation laws using a combination of cell averages and point values as independent degrees of freedom, based on ideas from fini…
On Enhancing the Dissipative Behavior of Active Flux Advection Schemes
Christian Klingenberg, Simon Krotsch, Philip Roe
In this work, the traditional third-order Active Flux advection scheme is modified by reformulating the method and introducing additional parameters. The effect of these parameters…
Local sensitivity-preserving random data down-sampling for experimental design
Kathrin Hellmuth, Christian Klingenberg, Qin Li
The quality of numerical reconstructions for unknown parameters in inverse problems depends fundamentally on the selection of experimental data. To ensure a robust reconstruction,…
On the equivalence of semi-discrete Active Flux and Discontinuous Galerkin methods and a comparison of their performance
Wasilij Barsukow, Christian Klingenberg, Simon Krotsch
The Active Flux (AF) method employs a globally continuous approximation, like continuous Finite Element methods. This is achieved through the placement of point values at cell inte…
A generalized Active Flux method of arbitrarily high order in two dimensions
Wasilij Barsukow, Praveen Chandrashekar, Christian Klingenberg +1
The Active Flux method can be seen as an extended finite volume method. The degrees of freedom of this method are cell averages, as in finite volume methods, and in addition shared…
An asymptotic-preserving active flux scheme for the hyperbolic heat equation in the diffusive scaling
Junming Duan, Wasilij Barsukow, Christian Klingenberg
The Active Flux (AF) method is a compact, high-order finite volume scheme that enhances flexibility by introducing point values at cell interfaces as additional degrees of freedom…