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math.NA2026
On the involution preserving properties of semi-discrete Active Flux methods on simplex
Remi Abgrall, Yongle Liu, Mario Ricchiuto
We study the involution-preserving properties of the Active Flux method on unstructured triangular meshes. Two model problems are considered: the two-dimensional linear acoustic sy…
math.NA2026
Invariant domain preservation for hybrid point-value and cell-average discretizations of hyperbolic equations on general meshes
Shengrong Ding, Shumo Cui, Remi Abgrall +1
This paper presents a unified invariant-domain-preserving (IDP) framework for hybrid discretizations of hyperbolic conservation laws, including active flux and PAMPA methods, in wh…
math.NA2026
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…