Oscillation-Eliminating (OE) Approach and its Variants | Kailiang Wu

BibTeX

COS(SV): Convex Oscillation-Suppressing Spectral Volume Schemes with Bound Preservation for Hyperbolic Conservation Laws

@article{pub2026cosdgaconvexoscillationsuppressingframeworkforhighorderdiscontinuousgalerkin,
  author = {Huihui Cao and Yunqing Huang and Zhuoyun Li and Kailiang Wu},
  title = {{COS(DG): A Convex Oscillation-Suppressing Framework for High-Order Discontinuous Galerkin Methods}},
  journal = {Journal of Computational Physics},
  year = {2026},
  volume = {554},
  pages = {114755},
  doi = {10.1016/j.jcp.2026.114755},
  url = {https://doi.org/10.1016/j.jcp.2026.114755}
}

R. Yan, H. Cao, N. Liu*, and K. Wu

Journal of Computational Physics, 2027.

BibTeX

Spectral volume from a discontinuous Galerkin perspective: oscillation elimination, stability, and optimal error estimates

@article{pub2026cossvconvexoscillationsuppressingspectralvolumeschemeswithboundpreservationfor,
  author = {Ruifang Yan and Huihui Cao and Na Liu and Kailiang Wu},
  title = {{COS(SV): Convex Oscillation-Suppressing Spectral Volume Schemes with Bound Preservation for Hyperbolic Conservation Laws}},
  journal = {Journal of Computational Physics},
  year = {2027},
  volume = {568},
  pages = {115411},
  doi = {10.1016/j.jcp.2026.115411},
  url = {https://doi.org/10.1016/j.jcp.2026.115411}
}

Z. Li and K. Wu*

SIAM Journal on Scientific Computing, 2025.

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Oscillation-eliminating central DG schemes on Cartesian meshes for hyperbolic conservation laws

@article{pub2024spectralvolumefromadgperspectiveoscillationeliminationstability,
  author = {Zhuoyun Li and Kailiang Wu},
  title = {{Spectral volume from a discontinuous Galerkin perspective: oscillation elimination, stability, and optimal error estimates}},
  journal = {SIAM Journal on Scientific Computing},
  year = {2025},
  volume = {47},
  number = {2},
  pages = {A1304-A1333},
  doi = {10.1137/24m167799x},
  eprint = {2409.10871},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1137/24m167799x}
}

M. Peng, K. Wu*, and C. Yuan

SIAM Journal on Scientific Computing, 2026.

BibTeX

High-order oscillation-eliminating Hermite WENO method for hyperbolic conservation laws

@article{pub2025oscillationeliminatingcentraldgschemesforhyperbolicconservationlaws,
  author = {Manting Peng and Kailiang Wu and Caiyou Yuan},
  title = {{Oscillation-eliminating central DG schemes on Cartesian meshes for hyperbolic conservation laws}},
  journal = {SIAM Journal on Scientific Computing},
  year = {2026},
  volume = {48},
  number = {2},
  pages = {A695-A725},
  doi = {10.1137/25m1730697},
  eprint = {2503.12473},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1137/25m1730697}
}

C. Fan and K. Wu*

Journal of Computational Physics, 2024.

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EPO: A Unified Framework for Entropy Stability, Positivity, and Oscillation Suppression

@article{pub2024highorderoscillationeliminatinghermitewenomethodforhyperbolic,
  author = {Chuan Fan and Kailiang Wu},
  title = {{High-order oscillation-eliminating Hermite WENO method for hyperbolic conservation laws}},
  journal = {Journal of Computational Physics},
  year = {2024},
  volume = {519},
  pages = {113435},
  doi = {10.1016/j.jcp.2024.113435},
  eprint = {2409.09632},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1016/j.jcp.2024.113435}
}

K. Wu

arXiv, 2026. Preprint

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Runge–Kutta-Aligned Oscillation Elimination: Restoring Superconvergence for Fully Discrete Shock-Capturing DG Schemes

@misc{pubarxiv260400301,
  author = {Kailiang Wu},
  title = {{EPO: A Unified Framework for Entropy Stability, Positivity, and Oscillation Suppression}},
  year = {2026},
  eprint = {2604.00301},
  archivePrefix = {arXiv},
  note = {Preprint},
  url = {https://arxiv.org/abs/2604.00301}
}

M. Peng, Z. Li, and K. Wu*

arXiv, 2026. Preprint

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Compact Finite-Average-Moment Schemes with Single-Step Oscillation Elimination for Hyperbolic Conservation Laws

@misc{pubarxiv260926195,
  author = {Manting Peng and Zhuoyun Li and Kailiang Wu},
  title = {{Runge--Kutta-Aligned Oscillation Elimination: Restoring Superconvergence for Fully Discrete Shock-Capturing DG Schemes}},
  year = {2026},
  eprint = {2609.26195},
  archivePrefix = {arXiv},
  note = {Preprint},
  url = {https://arxiv.org/abs/2609.26195}
}

C. Fan and K. Wu*

arXiv, 2026. Preprint

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Robust DG schemes on unstructured triangular meshes: Oscillation elimination and bound preservation via optimal convex decomposition

@misc{pubarxiv260926194,
  author = {Chuan Fan and Kailiang Wu},
  title = {{Compact Finite-Average-Moment Schemes with Single-Step Oscillation Elimination for Hyperbolic Conservation Laws}},
  year = {2026},
  eprint = {2609.26194},
  archivePrefix = {arXiv},
  note = {Preprint},
  url = {https://arxiv.org/abs/2609.26194}
}

S. Ding, S. Cui, and K. Wu*

Journal of Computational Physics, 2025.

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Uniformly high-order bound-preserving OEDG schemes for two-phase flows

@article{pub2025robustdgschemesonunstructuredtriangularmeshesoscillationelimination,
  author = {Shengrong Ding and Shumo Cui and Kailiang Wu},
  title = {{Robust DG schemes on unstructured triangular meshes: Oscillation elimination and bound preservation via optimal convex decomposition}},
  journal = {Journal of Computational Physics},
  year = {2025},
  eprint = {2409.09620},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2409.09620}
}

R. Yan, R. Abgrall, and K. Wu*

Math. Models Methods Appl. Sci. (M3AS), 2024.

BibTeX

Structure-preserving oscillation-eliminating discontinuous Galerkin schemes for ideal MHD equations: Locally divergence-free and positivity-preserving

@article{pub2024uniformlyhighorderboundpreservingoedgschemesfortwo,
  author = {R. Yan and R. Abgrall and K. Wu},
  title = {{Uniformly high-order bound-preserving OEDG schemes for two-phase flows}},
  journal = {Math. Models Methods Appl. Sci. (M3AS)},
  year = {2024},
  doi = {10.1142/S0218202524500544},
  url = {https://doi.org/10.1142/S0218202524500544}
}

M. Liu and K. Wu*

Journal of Computational Physics, 2025.

BibTeX

Robust discontinuous Galerkin methods maintaining physical constraints for general relativistic hydrodynamics

@article{pub2025structurepreservingoscillationeliminatingdiscontinuousgalerkinschemesforideal,
  author = {Mengqing Liu and Kailiang Wu},
  title = {{Structure-preserving oscillation-eliminating discontinuous Galerkin schemes for ideal MHD equations: Locally divergence-free and positivity-preserving}},
  journal = {Journal of Computational Physics},
  year = {2025},
  eprint = {2404.16794},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2404.16794}
}

H. Cao, M. Peng, and K. Wu*

Journal of Computational Physics, 2025.

BibTeX

Constraint-Preserving High-Order Compact OEDG Method for Spherically Symmetric Einstein-Euler System

@article{pub2025robustdiscontinuousgalerkinmethodsmaintainingphysicalconstraintsforgeneral,
  author = {Huihui Cao and Manting Peng and Kailiang Wu},
  title = {{Robust discontinuous Galerkin methods maintaining physical constraints for general relativistic hydrodynamics}},
  journal = {Journal of Computational Physics},
  year = {2025},
  eprint = {2410.05000},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2410.05000}
}

Y. Huang, M. Peng, and K. Wu*

Communications in Mathematical Research, 2025.

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Oscillation-eliminating discontinuous Galerkin methods for multicomponent chemically reacting flows

@article{pub2025constraintpreservinghighordercompactoedgmethodforsphericallysymmetriceinsteineuler,
  author = {Yuchen Huang and Manting Peng and Kailiang Wu},
  title = {{Constraint-Preserving High-Order Compact OEDG Method for Spherically Symmetric Einstein-Euler System}},
  journal = {Communications in Mathematical Research},
  year = {2025},
  volume = {41},
  number = {4},
  pages = {370--414},
  doi = {10.4208/cmr.2025-0052},
  eprint = {2512.03496},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.4208/cmr.2025-0052}
}

J. Du, C. Fan, and K. Wu

Annals of Applied Mathematics, 2024.

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Bound-preserving OEDG schemes for Aw–Rascle–Zhang traffic models on networks

@article{pub2024oscillationeliminatingdiscontinuousgalerkinmethodsformulticomponentchemicallyreactingflows,
  author = {J. Du and C. Fan and K. Wu},
  title = {{Oscillation-eliminating discontinuous Galerkin methods for multicomponent chemically reacting flows}},
  journal = {Annals of Applied Mathematics},
  year = {2024},
  volume = {40},
  pages = {412-444},
  doi = {10.4208/aam.oa-2024-0029},
  url = {https://doi.org/10.4208/aam.oa-2024-0029}
}

W. Chen, S. Cui*, K. Wu, and T. Xiong

Journal of Computational Physics, 2025.

BibTeX

Provably positivity-preserving, globally divergence-free central DG methods for ideal MHD system

@article{pub2024boundpreservingoedgmethodforawrasclezhangtraffic,
  author = {Wei Chen and Shumo Cui and Kailiang Wu and Tao Xiong},
  title = {{Bound-preserving OEDG schemes for Aw--Rascle--Zhang traffic models on networks}},
  journal = {Journal of Computational Physics},
  year = {2025},
  volume = {520},
  pages = {113507},
  doi = {10.1016/j.jcp.2024.113507},
  eprint = {2409.16269},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1016/j.jcp.2024.113507}
}

R. Yan, H. Cao, and K. Wu*

Math. Models Methods Appl. Sci. (M3AS), 2026. Accepted

BibTeX

An active-flux-type scheme for ideal MHD with provable positivity and a point-value-level discrete divergence-free constraint

@article{pub2026provablypositivitypreservinggloballydivergencefreecentraldgmethodsforidealmhd,
  author = {Ruifang Yan and Huihui Cao and Kailiang Wu},
  title = {{Provably positivity-preserving, globally divergence-free central DG methods for ideal MHD system}},
  journal = {Math. Models Methods Appl. Sci. (M3AS)},
  year = {2026},
  eprint = {2508.08913},
  archivePrefix = {arXiv},
  note = {Accepted},
  url = {https://arxiv.org/abs/2508.08913}
}

M. Liu, D. Pang, R. Abgrall, and K. Wu*

Journal of Computational Physics, 2026. In press

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