10 papers
Construction of entropy satisfying Active Flux-type methods
Remi Abgrall, Yongle Liu
This paper is devoted to the analysis of the entropy stability properties of Active Flux\yolo{-type} scheme for a hyperbolic system equipped with one entropy inequality. This type…
Robust PAMPA Scheme in the DG Formulation on Unstructured Triangular Meshes: bound preservation, oscillation elimination, and boundary conditions
Rémi Abgrall, Yongle Liu
We propose an improved version of the PAMPA algorithm where the solution is sought as globally continuous. The scheme is locally conservative, and there is no mass matrix to invert…
Some new properties of an Active flux type scheme: PamPa
Rémi Abgrall, Philipp Ãffner, Yongle Liu
In this paper, we provide a few new properties of Active Flux (AF)/Point-Average-Moment PolynomiAl-interpreted (\pampa) schemes. First, we show, in full generality, that the AF/pam…
Positivity-preserving Well-balanced PAMPA Schemes with Global Flux quadrature for One-dimensional Shallow Water Models
Remi Abgrall, Yongle Liu, Mario Ricchiuto
We present a novel hydrostatic and non-hydrostatic equilibria preserving Point-Average-Moment PolynomiAl-interpreted (PAMPA) method for solving the one-dimensional hyperbolic balan…
An active-flux-type scheme for ideal MHD with provable positivity and discrete divergence-free property
Mengqing Liu, Dongwen Pang, Remi Abgrall +1
We develop a positivity-preserving (PP) PAMPA (Point-Average-Moment PolynomiAl-interpreted) scheme that enforces a discrete divergence-free (DDF) magnetic field for ideal MHD on Ca…
Virtual finite element and hyperbolic problems: the PAMPA algorithm
Rémi Abgrall, Yongle Liu, Walter Boscheri
In this paper, we explore the use of the Virtual Element Method concepts to solve scalar and system hyperbolic problems on general polygonal grids. The new schemes stem from the ac…