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R. Fan, J. Koellermeier, Y. Xia, Y. Xu and J. Zhang, Well-balanced path-conservative discontinuous Galerkin methods with equilibrium preserving space for shallow water linearized moment equations, Journal of Scientific Computing, 108:2 (2026).
W. Hu and Y. Xia, Finite volume analysis of the Poisson problem via a reduced discontinuous Galerkin space, Communications on Applied Mathematics and Computation, to appear.
Y. Li, J. Cheng, Y. Xia and C.-W. Shu, On moving mesh WENO schemes with characteristic boundary conditions for Hamilton-Jacobi equations, Computers and Fluids, 205 (2020), 104582.
Y. Wan, S. Liu and Y. Xia, Convergence of the hybrid WENO scheme for steady compressible Navier-Stokes equations in curved geometries using Cartesian grids, Journal of Scientific Computing, 103:61 (2025).
Y. Li, J. Cheng, Y. Xia and C.-W. Shu, Direct arbitrary Lagrangian-Eulerian finite volume WENO method for single and multi-material flows, Communications in Computational Physics, to appear.
J.J.W. van der Vegt, Y. Xia and Y. Xu, Positivity preserving limiters for time-implicit higher order accurate discontinuous Galerkin discretizations, SIAM Journal on Scientific Computing, 41 (2019), pp. A2037-A2063.
C. Qiu, J. Hou, Y. Xia and L. Shan, A high order ensemble algorithm for dual-porosity-Navier-Stokes flows, Journal of Computational Physics, 520 (2025), 113498.
D. Xiao, J.X. Ma, Y. Li, Y. Xia and M.Y. Yu, Evolution of nonlinear dust-ion-acoustic waves in an inhomogeneous plasma, Physics of Plasmas , 13 (2006), 052308.
R. Guo, and Y. Xia, Arbitrary high-order fully-decoupled numerical schemes for phase-field models of two-phase incompressible flows, Communications on Applied Mathematics and Computation, 6 (2024), pp. 625-657.
F. Yan and Y. Xia, Analysis of average bound preserving time-implicit discretizations for convection-diffusion-reaction equation, Applied Numerical Mathematics, 211 (2025), pp. 103-122.
Y. Xia, A fully discrete stable discontinuous Galerkin method for the thin film epitaxy problem without slope selection, Journal of Computational Physics, 280 (2015), pp. 248-260.
L. Wei and Y. Xia, Steady-state simulation of Euler equations by the discontinuous Galerkin method with the hybrid limiter, Journal of Computational Physics, 515 (2024), 113288.
C. Jin, Y. Xia and Yan Xu, Kernel compensation method for Maxwell eigenproblem in photonic crystals with mimetic finite difference discretizations, Numerical Methods for Partial Differential Equations, 41:e23171 (2025).
L. Wei, and Y. Xia, Steady-state simulation of Euler equations by the discontinuous Galerkin method with the jump filter, Communications in Computational Physics, 39 (2026), pp. 1103–1136.
Z. Xue, Y. Xia, C. Li and X. Yuan, A simplified multilayer perceptron detector for the hybrid WENO scheme, Computers and Fluids, 244 (2022), 105584.
Y. Wan, and Y. Xia, A hybrid WENO scheme for steady-state simulations of Euler equations, Journal of Computational Physics, 463 (2022), 111292.
R. Guo, Y. Xia and Y. Xu, Semi-implicit spectral deferred correction methods for highly nonlinear partial differential equations, Journal of Computational Physics, 338 (2017), pp. 269-284.
Y. Wan, and Y. Xia, A hybrid WENO scheme for steady Euler equations in curved geometries on Cartesian grids, Communications in Computational Physics, 33 (2023), pp. 1270-1331.
X. Li and Y. Xia, ALE-Ritz projection in the analysis of moving mesh continuous/discontinuous Galerkin methods for convection-diffusion problems, Journal of Computational and Applied Mathematics, 486 (2026), 117678.
Y. Li, J. Cheng, Y. Xia and C.-W. Shu, High order arbitrary Lagrangian-Eulerian finite difference WENO scheme for Hamilton-Jacobi equations, Communications in Computational Physics, 26 (2019), pp. 1530-1574.
W. Zhang, Y. Xing, Y. Xia and Y. Xu, High-order positivity-preserving well-balanced discontinuous Galerkin methods for Euler equations with gravitation on unstructured meshes, Communications in Computational Physics, 32 (2022), pp. 771-815.
J. Zhang, Y. Xia and Y. Xu, Well-balanced path-conservative discontinuous Galerkin methods with equilibrium preserving space for two-layer shallow water equations, Journal of Computational Physics, 520 (2025), 113473.
J. Zhang, Y. Xia and Y. Xu, Equilliburm preserving space in discontinuous Galerkin methods for hyperbolic balance laws, Communications in Computational Physics, 38 (2025), pp. 109–155.
Y. Xia, Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for the Cahn-Hilliard type equations, Journal of Computational Physics, 227 (2007), pp. 472-491.
C. Sun, and Y. Xia, Asymptotic preserving spectral deferred correction methods for hyperbolic systems with relaxation, Communications in Computational Physics, 26 (2019), pp. 531-557.
P. Fu, and Y. Xia, The positivity preserving property on the high order arbitrary Lagrangian-Eulerian discontinuous Galerkin method for Euler equations, Journal of Computational Physics, 470 (2022), 111600.
J. Zhang, Y. Xia and Y. Xu, Well-balanced discontinuous Galerkin method with flux globalization for rotating shallow water equations, Journal of Computational Physics, 537 (2025), 114094.
Y. Xia, Y. Xu and C.-W. Shu, Efficient time discretization for local discontinuous Galerkin methods, Discrete and Continuous Dynamical Systems - Series B, 8 (2007), pp. 677-693.
J. Zhang, Y. Xia, and Y. Xu, Structure-preserving finite volume arbitrary Lagrangian-Eulerian WENO schemes for the shallow water equations, Journal of Computational Physics, 473 (2023), 111758.
X. Hong, and Y. Xia, Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for hyperbolic equations involving $\delta$-singularities, SIAM Journal on Numerical Analysis, 58 (2020), pp. 125-152.
C. Zhang, Y. Xu and Y. Xia, Local discontinuous Galerkin methods to a dispersive system of KdV-type equations, Journal of Scientific Computing, 86:4 (2021).
L. Huang, Y. Xia, S.C. Wong, C.-W. Shu, M. Zhang and W.H.K. Lam, A dynamic continuum model for bi-directional pedestrian flows, Proceedings of the Institution of Civil Engineers: Engineering and Computational Mechanics, 162 (2009), pp.67-75.
R. Guo, Y. Xia, and Y. Xu, An efficient fully-discrete local discontinuous Galerkin method for the Cahn-Hilliard-Hele-Shaw system, Journal of Computational Physics, 264 (2014), pp.23-40.
Q. Zhang, and Y. Xia, Discontinuous Galerkin methods for the Ostrovsky-Vakhnenko equation, Journal of Scientific Computing, 82:24 (2020).
S. Hou and Y. Xia, Discontinuous Galerkin method based on the reduced space for the nonlinear convection-diffusion-reaction equation, Journal of Scientific Computing, 99:19 (2024).
L. Wei and Y. Xia, An indicator-based hybrid limiter in discontinuous Galerkin methods for hyperbolic conservation laws, Journal of Computational Physics, 498 (2024), 112676.
S. Hou, Y. Chen and Y. Xia, A reduced basis warm-start iterative solver for the parameterized linear systems , Beijing Journal of Pure and Applied Mathematics, 2 (2025), pp. 123–146.
Z. Xue and Y. Xia, Exactly divergence-free ultra-weak discontinuous Galerkin method for incompressible flow, Communications on Applied Mathematics and Computation, to appear.
W. Zhang, Y. Xia and Y. Xu, Positivity-preserving well-balanced arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for the shallow water equations, Journal of Scientific Computing, 88:57 (2021).
S. Hou, Y. Chen, and Y. Xia, Fast L2 optimal mass transport via reduced basis methods for the Monge-Ampère equation, SIAM Journal on Scientific Computing, 44(6) (2022), A3536-A3559.
Y.Z. Tao, Y.Q. Jiang, J. Du, S.C. Wong, P. Zhang, Y.H. Xia, K. Choi, Dynamic system-optimal traffic assignment for a city using the continuum modeling approach, Journal of Advanced Transportation, 48 (2014), pp. 782-797.
Z. Xia and Y. Xia, Weighted essentially non-oscillatory generalized finite difference method for hyperbolic conservation laws, Journal of Computational Physics, 539 (2025), 114207.
L. Wei, L. Zhou and Y. Xia, The jump filter in the discontinuous Galerkin method for hyperbolic conservation laws, (arXiv version), Journal of Computational Physics, 520 (2025), 113498.
L. Wei, Q. Chen and Y. Xia, An efficient central discontinuous Galerkin scheme for hyperbolic conservation laws, Journal of Computational Physics, 548 (2026), 114566.
P. Fu, G. Schnücke, and Y. Xia, Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for conservation laws on moving simplex meshes, Mathematics of Computation, 88 (2019), pp. 2221-2255.
M. Wang, Y. Xia, Y. Xu and C.-W. Shu, A new ultraweak-local discontinuous Galerkin method for one-dimensional time-dependent sixth-order equations: optimal error estimates and superconvergence, International Journal of Numerical Analysis and Modeling, to appear.
W. Zhu, L.-L Feng, Y. Xia, C.-W. Shu, Q. Gu, and L.-Z. Fang, Turbulence in the intergalactic medium: solenoidal and dilatational motions and the impact of numerical viscosity, The Astrophysical Journal, 777:48 (2013).
Y. Xia, and Y. Xu, Weighted essentially non-oscillatory schemes for Degasperis-Procesi equation with discontinuous solutions, Annals of Mathematical Sciences and Applications, 2 (2017), pp. 319-340.
C. Zhang, Y. Xu and Y. Xia, Local discontinuous Galerkin methods for the μ-Camassa–Holm and μ-Degasperis–Procesi equations, Journal of Scientific Computing, 79 (2019), pp. 1294-1334.
Q. Tao, and Y. Xia, Error estimates and post-processing of local discontinuous Galerkin method for Schrödinger equations, Journal of Computational and Applied Mathematics, 356 (2019), pp. 198-218.
L. Yao, Y. Xia and Y. Xu, Semi-implicit low-stage deferred correction methods for the anisotropic phase-field dendritic crystal growth model, Computational and Applied Mathematics, 45:327, (2026).
C. Klingenberg, G. Schnücke, and Y. Xia, An arbitrary Lagrangian-Eulerian local discontinuous Galerkin method for Hamilton-Jacobi equations, Journal of Scientific Computing, 73 (2017), pp. 906-942.
Y. Liu, J. Lu, Q. Tao and Y. Xia, An oscillation-free discontinuous Galerkin method for shallow water equations, Journal of Scientific Computing, 92:109 (2022).
Y. Xia, Fourier spectral methods for Degasperis-Procesi equation with discontinuous solutions, Journal of Scientific Computing, 61 (2014), pp. 584-603.
L. Yao, Y. Xia and Y. Xu, High-order stabilization in the semi-implicit deferred correction methods, East Asian Journal on Applied Mathematics, to appear.
L. Zhou, Y. Xia, and C.-W. Shu, Stability analysis and error estimates of arbitrary Lagrangian-Eulerian discontinuous Galerkin method coupled with Runge-Kutta time-marching for linear conservation laws, ESAIM: Mathematical Modelling and Numerical Analysis, 53 (2019), pp. 105-144.
Y. Xia, Y. Xu, A conservative local discontinuous Galerkin method for the Schrödinger-KdV system, Communications in Computational Physics, 15 (2014), pp. 1091-1107.
L. Yao, Y. Xia and Y. Xu, L-stable spectral deferred correction methods and applications to phase field models, Applied Numerical Mathematics, 197 (2024), pp. 288-306.
Y. Xia, Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for the generalized Zakharov system, Journal of Computational Physics, 229 (2010), pp. 1238-1259.
R.-Y. Guo, S. C. Wong; Y. Xia, H.-J. Huang, W. H. K. Lam, and K. Choi, Empirical Evidence for the Look-Ahead Behavior of Pedestrians in Bi-directional Flows, Chinese Physics Letter, 29 (2012), 068901.
X. Zhang, Y. Xia and C.-W. Shu, Maximum-principle-satisfying and positivity-preserving high order discontinuous Galerkin schemes for conservation laws on triangular meshes, Journal of Scientific Computing, 50 (2012), pp.29-62.
F. Yan, J.J.W. van der Vegt, Y. Xia and Y. Xu, Higher order accurate bounds preserving time-implicit discretizations for the chemically reactive Euler equations, Communications in Computational Physics, 38 (2025), pp. 1017–1052.
Y. Wan and Y. Xia, A new hybrid WENO scheme with the high-frequency region for hyperbolic conservation laws, Communications on Applied Mathematics and Computation, 5 (2023), pp. 199-234.
W. Zhang, Y. Xing, Y. Xia and Y. Xu, High order structure-preserving arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for the Euler equations under gravitational fields, Computers and Mathematics with Applications, 146 (2023), pp. 339-359.
Y. Xia, Y. Xu and C.-W. Shu, Application of the local discontinuous Galerkin method for the Allen-Cahn/Cahn-Hilliard system, Communications in Computational Physics, 5 (2009), pp. 821-835.
Z. Xue, F. Yan and Y. Xia, Exactly divergence-free ultra-weak discontinuous Galerkin method for Brinkman-Forchheimer equations, Journal of Computational and Applied Mathematics, 477 (2026), 117124.
Q. Zhang, and Y. Xia, Discontinuous Galerkin methods for short pulse type equations via hodograph transformations, Journal of Computational Physics, 399 (2019), 108928.
J. Zhao, Q. Zhang, Y. Yang and Y. Xia, Conservative discontinuous Galerkin methods for the nonlinear Serre equations, Journal of Computational Physics, 421 (2020), 109729.
B. Li, Y. Xia and Z. Yang, Optimal convergence of arbitrary Lagrangian-Eulerian iso-parametric finite element methods for parabolic equations in an evolving domain, IMA Journal of Numerical Analysis, 43 (2023), pp. 501-534.
L. Zhou and Y. Xia, Arbitrary Lagrangian-Eulerian local discontinuous Galerkin method for linear convection-diffusion equations, Journal of Scientific Computing, 90:21 (2022).
F. Yan, J.J.W. van der Vegt, Y. Xia and Y. Xu, Entropy dissipative higher order accurate positivity preserving time-implicit discretizations for nonlinear degenerate parabolic equations, Journal of Computational and Applied Mathematics, 441 (2024), 115674.
Y. Xia, S.C. Wong and C.-W. Shu, Dynamic continuum pedestrian flow model with memory effect, Physical Review E, 79 (2009), article number 066113.
C. Klingenberg, G. Schnücke, and Y. Xia, Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for conservation laws: analysis and application in one dimension, Mathematics of Computation, 86 (2017), pp. 1203-1232.
Q. Zhang, and Y. Xia, Conservative and dissipative local discontinuous Galerkin methods for Korteweg-de Vries type equations, Communications in Computational Physics, 25 (2019), pp. 532-563.
Z. Cao, P. Fu, L.-W. Ji, and Y. Xia, Application of local discontinuous Galerkin method to Einstein equations, International Journal of Modern Physics D, 28 (2019), 1950014.
J. Zhang, Y. Xia, and Y. Xu, Moving water equilibria preserving discontinuous Galerkin method for the shallow water equations, Journal of Scientific Computing, 95:48 (2023).
L. Yao, Y. Xia and Y. Xu, Stability of implicit deferred correction methods based on BDF methods, Applied Mathematics Letters, 158 (2024), 109225.
X. Hong and Y. Xia, Arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for KdV type equations, Communications on Applied Mathematics and Computation, 4(2022), pp. 530-562 .
Y. Xia, S.C. Wong, M.P. Zhang, C.-W. Shu and W.H.K. Lam, An efficient discontinuous Galerkin method on triangular meshes for a pedestrian flow model, International Journal for Numerical Methods in Engineering, 76 (2008), pp. 337-350.
C. Klingenberg, F. Pörner, and Y. Xia, An efficient implementation of the divergence free constraint in a discontinuous Galerkin method for magnetohydrodynamics on unstructured meshes, Communications in Computational Physics, 21 (2017), pp. 423-442.
Publications in Proceedings
C. Klingenberg, G. Schnücke, and Y. Xia, An arbitrary Lagrangian-Eulerian discontinuous Galerkin method for conservation laws: Entropy stability, In: Klingenberg C., Westdickenberg M. (eds) Theory, Numerics and Applications of Hyperbolic Problems II. HYP 2016, pp. 209-219. Springer Proceedings in Mathematics & Statistics, vol 237. Springer, Cham.
J. Gallego, J. Loebbert, P. Bastian, C. Klingenberg, Y. Xia, Implementing a discontinuous Galerkin method for the compressible, inviscid Euler equations in the DUNE framework, Proceedings in Applied Mathematics and Mechanics, Vol. 14,1 (2014).
Y. Liang, Y. Xia and P. Bons, Grain growth and dissolution during crystal-melt interaction, Conference on Goldschmidt 2010 - Earth, Energy, and the Environment.
Y. Liang, A. Schiemenz, Y. Xia and M. Parmentier, High porosity harzburgite and dunite channels for the transport of compositionally heterogeneous melts in the mantle: II. Geochemical consequences, AGU Fall meeting, 2009.
Y. Xia, L. Huang, S.C. Wong, M. Zhang, C.-W. Shu and W.H.K. Lam, The follow-the-crowd effect in a pedestrian flow model, the Proceedings of the 12th International Conference of Hong Kong Society for Transportation Studies, December 2007, Hong Kong, pp.309-317.
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