most citedA positive- and bound-preserving vectorial lattice Boltzmann method in two dimensions

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math.NA2025

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…

math.NA2025

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…

math.NA2025

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…

math.NA2025

Some new properties of an Active flux type scheme: PamPa

Rémi Abgrall, Philipp Öffner, 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…

math.NA2025

Bound preserving {P}oint-{A}verage-{M}oment {P}olynomi{A}l-interpreted ({PAMPA}) on polygonal meshes

Rémi Abgrall, Yongle Liu, Walter Boscheri

We present a novel discretisation strategy, strongly inspired from Roe's Active Flux scheme. It can use polygonal meshes and is provably bound preserving for scalar problems and th…

math.NA2024

A Novel and Simple Invariant-Domain-Preserving Framework for PAMPA Scheme: 1D Case

Rémi Abgrall, Miaosen Jiao, Yongle Liu +1

The PAMPA (Point-Average-Moment PolynomiAl-interpreted) method, proposed in [R. Abgrall, Commun. Appl. Math. Comput., 5: 370-402, 2023], combines conservative and non-conservative…