Volume 57, Number 2, March-April 2023
|Page(s)||991 - 1027|
|Published online||07 April 2023|
Extensions of Active Flux to arbitrary order of accuracy
Institute for Mathematics and Computational Science, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
2 Institute for Mathematics, CNRS UMR 5251, University of Bordeaux, 351 Cours de la Libération, 33405 Talence, France
* Corresponding author: firstname.lastname@example.org
Accepted: 9 January 2023
Active Flux is a recently developed numerical method for hyperbolic conservation laws. Its classical degrees of freedom are cell averages and point values at cell interfaces. These latter are shared between adjacent cells, leading to a globally continuous reconstruction. The update of the point values includes upwinding, but without solving a Riemann Problem. The update of the cell average requires a flux at the cell interface, which can be immediately obtained using the point values. This paper explores different extensions of Active Flux to arbitrarily high order of accuracy, while maintaining the idea of global continuity. We propose to either increase the stencil while keeping the same degrees of freedom, or to increase the number of point values, or to include higher moments as new degrees of freedom. These extensions have different properties, and reflect different views upon the relation of Active Flux to the families of Finite Volume, Finite Difference and Finite Element methods.
Mathematics Subject Classification: 65M06 / 65M08 / 65M60 / 76N99
Key words: Active Flux / high order methods / conservation laws
© The authors. Published by EDP Sciences, SMAI 2023
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