Publications

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Journal Publications

  1. Yan Jiang, Chi-Wang Shu and Mengping Zhang, An alternative formulation of finite difference weighted ENO schemes with Lax-Wendroff time discretization for conservation laws, SIAM Journal on Scientific Computing, v35 (2013), pp. A1137-A1160.

  2. Yan Jiang, Chi-Wang Shu and Mengping Zhang, Free-stream preserving finite difference schemes on curvilinear meshes, Methods and Applications of Analysis, v21 (2014), pp. 1-30.

  3. Yan Jiang, Chi-Wang Shu and Mengping Zhang, High order finite difference WENO schemes with positivity-preserving limiter for correlated random walk with density-dependent turning rates, Mathematical Models and Methods in Applied Sciences (M3AS), v25 (2015), pp.1553-1588.

  4. Andrew Christlieb, Wei Guo and Yan Jiang, A WENO-based method of lines transpose approach for Vlasov simulations, Journal of Computational Physics, v327 (2016), pp. 337-367.

  5. Vrushali A. Bokil, Yingda Cheng, Yan Jiang and Fengyan Li, Energy stable discontinuous Galerkin methods for Maxwell's equations in nonlinear optical media, Journal of Computational Physics, v350 (2017), pp. 420-452.

  6. Vrushali A. Bokil, Yingda Cheng, Yan Jiang, Fengyan Li, and Puttha Sakkaplangkul, High spatial order energy stable FDTD methods for Maxwell's equations in nonlinear optical media, Journal of Scientific Computing, v77 (2018), pp. 1-42.

  7. Andrew Christlieb, Xiao Feng, Yan Jiang and Qi Tang, A high-order finite difference WENO scheme for ideal magnetohydrodynamics on curvilinear meshes, SIAM Journal on Scientific Computing, v40 (2018), pp. A2631-A2666.

  8. Andrew Christlieb, Wei Guo and Yan Jiang, A kernel based high order "explicit" unconditionally stable scheme for time dependent Hamilton-Jacobi equations, Journal of Computational Physics, v379 (2019), pp. 214-236.

  9. Andrew Christlieb, Wei Guo, Yan Jiang and Hyoseon Yang, A moving mesh WENO method based on exponential polynomials for one-dimensional conservation laws, Journal of Computational Physics, v380 (2019), pp. 334-354.

  10. Yan Jiang, Puttha Sakkaplangkul, Vrushali A. Bokil, Yingda Cheng and Fengyan Li, Dispersion analysis of finite difference and discontinuous Galerkin schemes for Maxwell's equations in linear Lorentz media, Journal of Computational Physics, v394 (2019), pp. 100-135.

  11. Yize Yu, Yan Jiang and Mengping Zhang, Free-stream preserving finite difference schemes for ideal magnetohydrodynamics on curvilinear meshes, Journal of Scientific Computing, v82 (2020), 23.

  12. Andrew Christlieb, Wei Guo, Yan Jiang and Hyoseon Yang, Kernel based high order "explicit" unconditionally stable scheme for nonlinear degenerate advection-diffusion equations, Journal of Scientific Computing, v82 (2020), 52.

  13. Yan Jiang, High order finite difference multi-resolution WENO method for nonlinear degenerate parabolic equations, Journal of Scientific Computing, v86 (2021), 16.

  14. Kaipeng Wang, Andrew Christlieb, Yan Jiang and Mengping Zhang, A kernel based unconditionally stable scheme for nonlinear parabolic partial differential equations, Communications in Computational Physics, v29 (2021), pp. 237-264.

  15. Zhanjing Tao, Yan Jiang and Yingda Cheng, An adaptive high-order piecewise polynomial based sparse grid collocation method with applications, Journal of Computational Physics, v433 (2021), 109770.

  16. Firat Cakir, Andrew Christlieb and Yan Jiang, A high order finite difference weighted essentially nonoscillatory scheme with a kernel-based constrained transport method for ideal magnetohydrodynamics, SIAM Journal on Scientific Computing, v43 (2021), pp. B598-B622.

  17. Ziqiang Cheng, Shihao Liu, Yan Jiang, Jianfang Lu, Mengping Zhang and Shuhai Zhang, A high order boundary scheme to simulate a complex moving rigid body under the impingement of a shock wave, Applied Mathematics and Mechanics (English Edition), v42 (2021), pp. 841-854.

  18. Kaipeng Wang, Yan Jiang and Mengping Zhang, A hybrid HWENO-based method of lines transpose approach for Vlasov simulations (English), Journal of University of Science and Technology of China, v51 (2021), pp. 202-215.

  19. Shihao Liu, Zhiqiang Cheng, Yan Jiang, Jianfang Lu, Mengping Zhang and Shuhai Zhang, Numerical simulation of a complex moving rigid body under the impingement of a shock wave in 3D, Advances in Aerodynamics, v4 (2022).

  20. Mengjiao Jiao, Yan Jiang, Chi-Wang Shu and Mengping Zhang, Optimal error estimates to smooth solutions of the central discontinuous Galerkin methods for nonlinear scalar conservation laws, ESAIM: Mathematical Modelling and Numerical Analysis, v56 (2022), pp. 1401 - 1435.

    21. Here is a supplementary material of the detailed proofs and formulas for Proposition 2.1 and Lemma 3.2.

  21. Zepeng Liu, Yan Jiang, Mengping Zhang and Qingyuan Liu, High order finite difference WENO method for shallow water equations on curvilinear meshes, Communications on Applied Mathematics and Computation, v5(2023), pp. 485-528.

  22. Shihao Liu, Yan Jiang, Chi-Wang Shu, Mengping Zhang and Shuhai Zhang, A high order moving boundary treatment for convection-diffusion equations, Journal of Computational Physics, v473 (2023), 111752.

  23. Qi Tao, Yong Liu, Yan Jiang, and Jianfang Lu, An oscillation free local discontinuous Galerkin method for nonlinear degenerate parabolic equations, Numerical Methods for Partial Differential Equations, v39 (2023), pp. 3145-3169.

  24. Lei Yang, Yuan Liu, Yan Jiang and Mengping Zhang, Discontinuous Galerkin methods for network patterning phase-field models, Journal of Scientific Computing, v98 (2024), 27.

  25. Mengjiao Jiao, Yan Jiang, and Mengping Zhang, A provable positivity-preserving local discontinuous Galerkin method for the viscous and resistive MHD equations, Communications on Applied Mathematics and Computation, v6(2024), pp. 279-310.

  26. Lei Yang, Shun Li, Yan Jiang, Chi-Wang Shu and Mengping Zhang, Inverse Lax-Wendroff boundary treatment of discontinuous Galerkin method for 1D conservation laws, Communications on Applied Mathematics and Computation, v7(2025), pp. 796-826.

  27. Jianfang Lu, Yan Jiang, Chi-Wang Shu and Mengping Zhang, Analysis of a class of spectral volume methods for linear scalar hyperbolic conservation laws, Numerical Methods for Partial Differential Equations, (2024), e23126.

  28. Guangyao Zhu, Yan Jiang and Mengping Zhang, Inverse Lax-Wendroff boundary treatment for solving conservation laws with finite volume methods, Communications on Applied Mathematics and Computation (2024).

  29. Shihao Liu, Tingting Li, Ziqiang Cheng, Yan Jiang, Chi-Wang Shu and Mengping Zhang, A new type of simplified inverse Lax-Wendroff boundary treatment I: hyperbolic conservation laws, Journal of Computational Physics, v514 (2024), 113259.

  30. Yan Jiang and Siyang Wang, Upwind summation-by-parts finite differences: error estimates and WENO methodology, Journal of Scientific Computing, v100 (2024).

  31. Peng Peng, Xin Tao, Zong Peng, Yan Jiang, Zhiming Gao, Di Yang, Jay M. Albert, Anthony A. Chan, Modeling radiation belt dynamics using a positivity-preserving finite volume method on general meshes, Journal of Geophysical Research: Space Physics, 129 (2024), e2024JA032919.

  32. Yuchang Liu, Yan Jiang and Mengping Zhang, Globally divergence-free spectral-DG methods for MHD equations on cylindrical coordinates, Beijing Journal of Pure and Applied Mathematics, v2(2025), pp. 285-324.

  33. Hu Yu, Ziqiang Cheng, Yan Jiang and Mengping Zhang, ILW boundary treatment for computational aeroacoustics with solid wall boundary conditions, Beijing Journal of Pure and Applied Mathematics, v2(2025), pp. 423-459.

  34. Yuchang Liu, Wei Guo, Yan Jiang and Mengping Zhang, Non-oscillatory entropy stable DG schemes for hyperbolic conservation law, Journal of Computational Physics, v531(2025), 113926.

  35. Zepeng Liu, Yan Jiang, Chi-Wang Shu and Mengping Zhang, High order inverse Lax-Wendroff procedure for fluid-structure interaction problems, Journal of Computational Physics, v531(2025), 113942.

  36. Yuchang Liu, Wei Guo, Yan Jiang and Mengping Zhang, Structure-preserving nodal DG method for the Euler equations with gravity: well-balanced, entropy stable, and positivity preserving, Journal of Computational Physics, v537(2025), 114095.

  37. Yuchang Liu, Wei Guo, Yan Jiang and Mengping Zhang, A globally divergence-free entropy stable nodal DG method for conservative ideal MHD equations, Journal of Computational Physics, v543(2025), 114382.

  38. Hu Yu, Zhiqiang Cheng and Yan Jiang, Global spectral analysis of two fully discrete discontinuous Galerkin methods on unfitted meshes, Journal of Scientific Computing, v105(2025), 54.

  39. Yuchang Liu, Yan Jiang and Mengping Zhang, Arbitrarily high-order globally divergence-free DG method for compressible ideal MHD equations on unstructured meshes, Journal of Scientific Computing, v105(2025), 85.

  40. Guangyao Zhu, Yan Jiang, Zhuang Zhao and Mengping Zhang, Inverse Lax-Wendroff boundary treatment for solving conservation laws with finite difference HWENO methods, Journal of Computational Physics, v547(2026), 114552.

  41. Shun Li and Yan Jiang, High-Order Implicit Low-Rank Method with Spectral Deferred Correction for Matrix Differential Equations, Journal of Scientific Computing, v106(2026), 75.

  42. Yangxin Fu, Yan Jiang and Siyang Wang, An energy-based discontinuous Galerkin method for the wave equation with nonsmooth solutions, Journal of Computational Physics, v557(2026), 114824.



Conference Proceedings
  1. Bo Dong, Sigal Gottlieb, Yulia Hristova, Yan Jiang and Haijin Wang, The effect of the sensitivity parameter in weighted essentially non-oscillatory methods, In S. Brenner (Ed.), Topics in Numerical Partial Differential Equations and Scientific Computing, The IMA Volumes in Mathematics and its Applications, vol. 160, Springer New York, 2016, pp. 23-50.


Preprints

  1. Lei Yan, Yan Jiang, and Chi-Wang Shu, Post-processing reduced-order models for transport-dominated problems by Gegenbauer reconstruction, submitted, 2025.

  2. Tingting Li and Yan Jiang, Stability analysis of a new type of inverse Lax-Wendroff boundary treatment of central difference schemes for parabolic equations, submitted, 2025.

  3. Yuchang Liu, Wei Guo, Yan Jiang and Mengping Zhang, Structure-preserving nodal DG method for Euler equations with gravity II: general equilibrium states, submitted, 2025.

  4. Yuchang Liu, Wei Guo, Yan Jiang and Zheng Sun, A limiter-based approach to construct high-order fully-discrete entropy stable explicit DG schemes for hyperbolic conservation laws, submitted, 2026.

  5. Shun Li, Yan Jiang, Mengping Zhang and Tao Xiong, Temporal-Stability-Enhanced and Energy-Stable Dynamical Low-Rank Approximation for Multiscale Linear Kinetic Transport Equations, submitted, 2026.

  6. Xiaopei Cheng, Fengna Yan, Yan Jiang and Ziqiang Cheng, Design and Analysis of Upwind-Biased Discontinuous Galerkin Methods with Optimal Dispersion Properties, submitted, 2026.