A new transported acoustic increment reconstruction in the Active Flux framework yields third-order accuracy and exact unsplit frozen evolution for the compressible Euler equations.
Barsukow,Semi-discrete Active Flux as a Petrov-Galerkin method, arXiv preprint arXiv:2508.15017, (2025)
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An enhanced globally continuous PAMPA scheme in DG form on triangular meshes adds non-oscillatory behavior to prior bound-preserving techniques, implements rigorous boundary conditions, and achieves third-order accuracy for smooth solutions per truncation analysis and tests.
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Fully Discrete Active Flux Method based on Transported Acoustic Increments for the Compressible Euler Equations
A new transported acoustic increment reconstruction in the Active Flux framework yields third-order accuracy and exact unsplit frozen evolution for the compressible Euler equations.
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Robust PAMPA Scheme in the DG Formulation on Unstructured Triangular Meshes: bound preservation, oscillation elimination, and boundary conditions
An enhanced globally continuous PAMPA scheme in DG form on triangular meshes adds non-oscillatory behavior to prior bound-preserving techniques, implements rigorous boundary conditions, and achieves third-order accuracy for smooth solutions per truncation analysis and tests.