Some new properties of the PamPa scheme

2025/08/23 by Abgrall, Rémi, Öffner, Philipp, Liu, Yongle · 1 citation
#35L40 #65M08 #76M10 #76M12 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2508.17147

Abstract

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 Active Flux (AF)/Point-Average-Moment PolynomiAl-interpreted (PAMPA) schemes can be interpreted in such a way that the discontinuous Galerkin (dG) scheme is one of their building blocks. Secondly we provide some intrinsic bound preserving properties. This is also illustrated numericaly. Last, we show, at least in one dimension, that the PAMPA scheme has the Summation by part property.

Citations

• Robust PAMPA Scheme in the DG Formulation on Unstructured Triangular Meshes: bound preservation, oscillation elimination, and boundary conditions
• Semi-discrete Active Flux as a Petrov-Galerkin method: the case of one-dimensional and Cartesian grids
• Stability of the Active Flux Method in the Framework of Summation-by-Parts Operators
• A generalized Active Flux method of arbitrarily high order in two dimensions
• Virtual finite element and hyperbolic problems: the PAMPA algorithm
• Bound preserving Point-Average-Moment PolynomiAl-interpreted (PAMPA) scheme: one-dimensional case
• Active flux for triangular meshes for compressible flows problems
• A New Approach for Designing Well-Balanced Schemes for the Shallow Water Equations: A Combination of Conservative and Primitive Formulations
• Extensions of Active Flux to arbitrary order of accuracy
• The Cartesian Grid Active Flux Method with Adaptive Mesh Refinement
• A combination of Residual Distribution and the Active Flux formulations or a new class of schemes that can combine several writings of the same hyperbolic problem: application to the 1D Euler equations
• The Active Flux scheme for nonlinear problems
• The active flux scheme on Cartesian grids and its low Mach number limit

Cited by

• Robust PAMPA Scheme in the DG Formulation on Unstructured Triangular Meshes: bound preservation, oscillation elimination, and boundary conditions

Related

• Bound preserving Point-Average-Moment PolynomiAl-interpreted (PAMPA) scheme: one-dimensional case
• A Novel and Simple Invariant-Domain-Preserving Framework for PAMPA Scheme: 1D Case
• A Novel and Simple Invariant-Domain-Preserving Framework for PAMPA Scheme: 1D Case
• Bound preserving Point-Average-Moment PolynomiAl-interpreted (PAMPA) on polygonal meshes
• Robust PAMPA Scheme in the DG Formulation on Unstructured Triangular Meshes: bound preservation, oscillation elimination, and boundary conditions