National outstanding youth fund winner
Publications in Refereed Journals (Appeared or Accepted)
1. Y. Xu, The convergence and stability of difference solutions for Burgers-KdV equation (in Chinese), Journal of Tianjin Normal University (Natural Science Edition), 22 (2002), pp.33-37.
2. Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for three classes of nonlinear wave equations, Journal of Computational Mathematics, 22 (2004), pp.250-274.
3. Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for nonlinear Schrodinger equations , Journal of Computational Physics, 205 (2005), pp.72-97.
4. Y. Xu, The convergence and stability of difference solutions for a class of coupled KdV equation (in Chinese), Journal of Engineering Mathematics, 22(2005), pp.47-52.
5. Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for two classes of two dimensional nonlinear wave equations , Physica D, 208 (2005), pp.21-58.
6. Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for the Kuramoto-Sivashinsky equations and the Ito-type coupled KdV equations , Computer Methods in Applied Mechanics and Engineering, 195 (2006), pp. 3430-3447.
7. Y. Xu and C.-W. Shu, Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations, Computer Methods in Applied Mechanics and Engineering, 196 (2007), pp.3805-3822.
8. J.J.W. van der Vegt and Y. Xu, Space-time discontinuous Galerkin method for nonlinear water waves, Journal of Computational Physics, 224 (2007), pp.17-39.
9. 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.
10. 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.
11. Y. Xu and C.-W. Shu, A local discontinuous Galerkin method for the Camassa-Holm equation, SIAM Journal on Numerical Analysis, 46 (2008), pp.1998-2021.
12. Y. Xu, J.J.W. van der Vegt and O. Bokhove, Discontinuous Hamiltonian finite element method for linear hyperbolic systems, Journal of Scientific Computing, 35 (2008), pp.241-265.
13. Y. Xu and C.-W. Shu, Local discontinuous Galerkin method for the Hunter-Saxton equation and its zero-viscosity and zero-dispersion limit, SIAM Journal on Scientific Computing, 31 (2008), pp. 1249-1268
14. 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.
15. Y. Xu and C.-W. Shu, Local discontinuous Galerkin method for surface diffusion and Willmore flow of graphs, Journal of Scientific Computing, 40 (2009), pp.375-390.
16. Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for high-order time-dependent partial differential equations, Communications in Computational Physics, 7 (2010), pp. 1-46.
17. 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.
18. Y. Xu and C.-W. Shu, Dissipative numerical methods for the Hunter-Saxton equation , Journal of Computational Mathematics, 28(2010), pp.606-620.
19. L. Ji and Y. Xu, Optimal error estimates of the local discontinuous Galerkin method for Willmore flow of graphs on Cartesian meshes, International Journal of Numerical Analysis & Modeling, 8(2011), pp.252-283.
20. Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for the Degasperis-Procesi equation, Communications in Computational Physics, 10(2011), pp. 474-508.
21. Y. Xu and C.-W. Shu, Optimal error estimates of the semi-discrete local discontinuous Galerkin methods for high order wave equations, SIAM Journal on Numerical Analysis, 50(2012), pp. 79-104.
22. L. Ji and Y. Xu, Optimal error estimates of the local discontinuous Galerkin method for surface diffusion of graphs on Cartesian meshes, Journal of Scientific Computing, 51(2012), pp.1-27.
23. X.Z. Li, Y. Xu and Y.S. Li, Investigation of multi-soliton, multi-cuspon solutions and their interaction of the Camassa-Holm equation, Chinese Annals of Mathematics, Series B, 33B(2012), pp.225-246.
24. L. Ji, Y. Xu and J.K. Ryan, Accuracy-enhancement of discontinuous Galerkin solutions for convection-diffusion equations in multiple-dimensions, Mathematics of Computation, 81(2012), pp.1929-1950.
25. L. Ji, Y. Xu and J.K. Ryan, Negative order norm estimates for nonlinear hyperbolic conservation laws, Journal of Scientific Computing, 54(2013), pp.531-548.
26. J. Jiang and Y. Xu, Local discontinuous Galerkin method for the impact-induced wave in a slender cylinder composed of a non-convex elastic material, Communications in Mathematics and Statistics, 1 (2013), pp.393-415.
27. R. Guo and Y. Xu, Efficient solvers of discontinuous Galerkin discretization for the Cahn-Hilliard equations, Journal of Scientific Computing, 58(2014), pp.380-408.
28. J. Jiang, Y. Xu, D. Dai, A dissipation-rate reserving DG method for wave catching-up phenomena in a nonlinearly elastic composite bar, Journal of Computational Physics, 258(2014), pp. 405-430.
29. L. Guo and Y. Xu, Local discontinuous Galerkin methods for the 2D simulation of quantum transport phenomena, Communications in Computational Physics, 15(2014), pp. 1012-1028.
30. Y. Xia and Y. Xu, Conservative local discontinuous Galerkin methods for the Schoedinger-KdV system, Communications in Computational Physics, 15(2014), pp. 1091-1107.
31. 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.
32. L. Tian, Y. Xu, J.G.M. Kuerten and J.J.W. Van der Vegt, A local discontinuous Galerkin method for the propagation of phase transition in solids and fluids, Journal of Scientific Computing, 59 (2014), pp.688-720.
33. F. Zhang, Y. Xu, F. Chen, Discontinuous Galerkin Methods for Isogeometric Analysis for Elliptic Equations on Surfaces, Communications in Mathematics and Statistics, 2(2014), pp.431-461.
34. R. Guo and Y. Xu, Fast solver for the local discontinuous Galerkin discretization of the KdV type equations, Communications in Computational Physics, 17(2015), pp. 424-457.
35. R. Guo, Y. Xu and Z. Xu, Local discontinuous Galerkin methods for the functionalized Cahn-Hilliard equation, Journal of Scientific Computing, 63(2015), pp 913-937.
36. L. Tian, Y. Xu, J.G.M. Kuerten and J.J.W. Van der Vegt, A local discontinuous Galerkin method for the (non)-isothermal Navier-Stokes-Korteweg equations, Journal of Computational Physics, 295(2015), pp.685-714.
37. R. Guo and Y. Xu, An efficient, unconditionally energy stable local discontinuous Galerkin scheme for the Cahn-Hilliard-Brinkman system, Journal of Computational Physics, 298(2015), pp.387-405.
38. L. Guo, Y. Xu, Z. Xu and J. Jiang, A PDE-based Regularization Algorithm toward Reducing Speckle Tracking Noise: A Feasibility Study for Ultrasound Breast Elastography, Ultrasonic Imaging, 37(2015), pp.277-293.
39. L. Guo and Y. Xu, Energy conserving local discontinuous Galerkin methods for the nonlinear Schrodinger equation with wave operator, Journal of Scientific Computing, 65(2015), pp.622-647.
40. F. Zhang, Y. Xu, F. Chen, R. Guo, Interior Penalty Discontinuous Galerkin Based Isogeometric Analysis for Allen-Cahn Equations on Surfaces, Communications in Computational Physics, 18(2015), pp.1380-1416.
41. R. Guo, L. Ji and Y. Xu, High order local discontinuous Galerkin methods for the Allen-Cahn equation: analysis and simulation, Journal of Computational Mathematics, 34(2016), pp.135-158.
42. R. Guo and Y. Xu, Local discontinuous Galerkin method and high order semi-implicit scheme for the phase field crystal equation, SIAM Journal on Scientific Computing, 38(2016), pp.A105-A127.
43. R. Guo, F. Filbet and Y. Xu, Efficient high order semi-implicit time discretization and local discontinuous Galerkin methods for highly nonlinear PDEs, Journal of Scientific Computing, 68(2016), pp.1029-1054.
44. L. Tian, Y. Xu, J.G.M. Kuerten and J.J.W. Van der Vegt, An h-adaptive local discontinuous Galerkin method for the Navier-Stokes-Korteweg equations, Journal of Computational Physics, 319(2016), pp.242-265.
45. Z. Lu, A. Cesmelioglu, J.J.W. Van der Vegt, Y. Xu, Discontinuous Galerkin approximations for computing electromagnetic bloch modes in photonic crystals, Journal of Scientific Computing70(2017), pp.922-964.
46. 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.
47. F. Zhang, Y. Xu, F. Chen, Discontinuous Galerkin Based Isogeometric Analysis for Geometric flows, Journal of Scientific Computing, 71(2017), pp.525-546.
48. 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.
49. L. Zhou, Y. Xu, Z. Zhang, W. Cao, Superconvergence of local discontinuous Galerkin method for one-dimensional linear Schrodinger equations, Journal of Scientific Computing 73(2017), pp.1290-1315.
50. R. Guo and Y. Xu, An adaptive time-stepping strategy and local discontinuous Galerkin method for the modified phase field crystal equation, Communications in Computational Physics, 24(2018), pp.123-151 .
51. L. Zhou and Y. Xu, Stability analysis and error estimates of semi-implicit spectral deferred correction coupled with local discontinuous Galerkin method for linear convection-diffusion equations, Journal of Scientific Computing, 77(2018), pp.1001-1029.
52. T. Ma and Y. Xu, Local discontinuous Galerkin methods for the two-dimensional Camassa-Holm equation. Communications in Mathematics and Statistics, 6(2018), pp.359-388.
53. Z. Lu, J.J.W. Van der Vegt, Y. Xu, Spectral approximation for polynomial eigenvalue problems, Computers and Mathematics with Applications, 76(2018), pp.1184-1197.
54. P. Fu, F. Li and Y. Xu, Globally divergence-free discontinuous Galerkin methods for ideal magnetohydrodynamics equations, Journal of Scientific Computing, 77(2018), pp.1621-1659.
55. R. Guo and Y. Xu, Semi-implicit spectral deferred correction method based on the invariant energy quadratization approach for phase field problems, Communications in Computational Physics, 26(2019), pp.87-113.
56. P. Fu, Y. Cheng, F. Li and Y. Xu, Discontinuous Galerkin Methods with Optimal L2 Accuracy for PDEs with High Order Spatial Derivatives, Journal of Scientific Computing, 78(2019), pp.816-863.
57. R. Guo and Y. Xu, Efficient, accurate and energy stable discontinuous Galerkin methods for phase field models of two-phase incompressible flows, Communications in Computational Physics, 26(2019), pp.1224-1248.
58. C. Zhang, Y. Xu and Y. Xia, Local discontinuous Galerkin methods for the $\mu$-Camassa-Holm and $\mu$-Degasperis-Procesi equations, Journal of Scientific Computing, 79(2019), pp.1294-1334.
59. 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.
60. Q. Tao and Y. Xu, Superconvergence of Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Methods for Linear Hyperbolic Equations, SIAM Journal on Numerical Analysis, 57(2019), pp.2142-2165.
61. R. Guo and Y. Xu, High order numerical simulations for the binary fluid-surfactant system using the discontinuous Galerkin and spectral deferred correction methods, SIAM Journal on Scientific Computing, 42(2020), pp.B353-B378.
62. F. Yan and Y. Xu, Stability Analysis and Error Estimates of Local Discontinuous Galerkin Method with Semi-Implicit Spectral Deferred Correction Time-Marching for the Allen-Cahn Equation, Journal of Computational and Applied Mathematics, 376(2020), 112857.
63. Q. Tao, Y. Xu and C.-W. Shu, An ultraweak-local discontinuous Galerkin method for PDEs with high order spatial derivatives, Mathematics of Computation, 89(2020), 2753-2783.
64. Q. Tao, Y. Xu and C.-W. Shu, A discontinuous Galerkin method and its error estimate for nonlinear fourth-order wave equations, Journal of Computational and Applied Mathematics, 386(2021), 113230.
65. C. Zhang, Y. Xu and Y. Xia, Local discontinuous Galerkin methods to a dispersive system of KdV-type equations, Journal of Scientific Computing, 86(2021), Article number:4.
66. Q. Zhang, Y. Xu and C.-W. Shu, Dissipative and conservative local discontinuous Galerkin methods for the Fornberg-Whitham type equations, Communications in Computational Physics, 30 (2021), pp. 321-356.
67. Q. Kang and Y. Xu, A discontinuous Galerkin method with minimal dissipation for a finite-strain plate, Advances in Applied Mathematics and Mechanics, 13 (2021), pp. 1027-1063.
68. F. Yan and Y. Xu, Error analysis of an unconditionally energy stable local discontinuous Galerkin scheme for the Cahn-Hilliard equation with concentration dependent mobility, Computational Methods in Applied Mathematics, 21 (2021), pp. 729-751.
69. 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(2021), Article number: 57.
70. Q. Tao, Y. Xu and X. Li, Negative norm estimates for arbitrary Lagrangian-Eulerian discontinuous Galerkin method for nonlinear hyperbolic equations, Communications on Applied Mathematics and Computation, 4 (2022), pp. 250-270.
71. 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, 31 (2022), pp. 771-815. .
72. J. Lin, Y. Xu, H. Xu, X. Zhong, High order finite difference WENO methods with unequal-sized sub-stencils for the Degasperis-Procesi type equations , Communications in Computational Physics, 31 (2022), pp. 913-946.
73. X. Meng, Y. Xu, Adaptive local discontinuous Galerkin methods with semi-implicit time discretizations for the Navier-Stokes equations, Advances in Aerodynamics, 4(2022), Article number: 22.
74. X. Yu, Y. Xu, Q. Du, Asymptotically compatible approximations of linear nonlocal conservation laws with variable horizon, Numerical Methods for Partial Differential Equations, 38 (2022), pp. 1948-1966.
75. X. Yu, Y. Xu, Q. Du, Numerical simulation of singularity propagation modeled by linear convection equations with spatially heterogeneous nonlocal interactions, Journal of Scientific Computing, 92(2022), Article number: 59.
76. Z. Lu and Y. Xu, A parallel eigensolver for photonic crystals discretized by edge finite elements, Journal of Scientific Computing, 92(2022), Article number: 79.
77. Q. Tao, L. Ji, J.K. Ryan, Y. Xu, Accuracy-enhancement of discontinuous Galerkin methods for PDEs containing high order spatial derivatives, Journal of Scientific Computing, 93(2022), Article number: 13.
78. J. Lu, Y. Xu, C. Zhang, Error estimates of the local discontinuous Galerkin methods for two-dimensional ($\mu$)-Camassa-Holm equations, Journal of Computational and Applied Mathematics, 420 (2023), Article number: 114722.
79. 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), Article number: 111758.
80. J. Zhang, Y. Xia and Y. Xu, Moving equilibria preserving DG method for shallow water equations, Journal of Scientific Computing, 95 (2023), Article number: 48.
81. Q. Zhang, Y. Xu and Y. Liu, A discontinuous Galerkin method for the generalized Camassa-Holm-Kadomtsev-Petviashvili equation, Numerical Methods for Partial Differential Equations, 39 (2023), pp. 3609-3633.
82. 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.
83. F. Wang, Q. Tao and Y. Xu, The local discontinuous Galerkin method for the nonlinear quantum Zakharov system, Journal of Computational and Applied Mathematics, 436 (2024), Article number: 115416.
84. 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), Article number: 115674.
85. R. Guo and Y. Xu, Semi-implicit spectral deferred correction methods based on second order time integration schemes for nonlinear PDEs, Journal of Computational Mathematics, 42(2024), pp.111-133.
86. 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.
87. X. Cheng, J.J.W. van der Vegt, Y. Xu and H.J. Zwart, Port-Hamiltonian formulations of the incompressible Euler equations with a free surface, Journal of Geometry and Physics, 197(2024), Article number: 105097.
88. W. Zheng and Y. Xu, High order decoupled and bound preserving local discontinuous Galerkin methods for a class of chemotaxis models, Communications on Applied Mathematics and Computation, 6(2024), pp.372-398.
89. L. Yao, Y. Xia and Y. Xu, Stability of Implicit Deferred Correction Methods Based on BDF methods, Applied Mathematics Letters, 158 (2024), 109225.
90. 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), Article number: 113473.
91. J. Lu, Q. Tao and Y. Xu, A coupled high-order continuous and discontinuous Galerkin finite element scheme for the Davey-Stewartson system, Communications in Computational Physics, to appear.
92. 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, to appear.
93. M. Wang and Y. Xu, Superconvergence of ultraweak-local discontinuous Galerkin methods for one-dimensional sixth order equations, Communications on Applied Mathematics and Computation, to appear.
94. J. Zhang, Y. Xia and Y. Xu, Equilliburm preserving space in discontinuous Galerkin methods for hyperbolic balance laws, Communications in Computational Physics, to appear.
95. W. Zheng and Y. Xu, Invariants preserving time-implicit local discontinuous Galerkin schemes for high-order nonlinear wave equations, Communications on Applied Mathematics and Computation, to appear.
96. Y. Wu and Y. Xu, A High-Order Local Discontinuous Galerkin Method for the p-Laplace Equation, Beijing Journal of Pure and Applied Mathematics, to appear.
97. X. Meng, Y. Xu and J.J.W. van der Vegt, Energy conservative local discontinuous Galerkin methods for the Euler-Korteweg equations, Advances in Applied Mathematics and Mechanics, to appear.
Publications in Refereed Proceedings
1. Y. Xu and C.-W. Shu, Preliminary results in local discontinuous Galerkin methods for two classes of 2D nonlinear wave equations (Abstract), in Abstracts of the Papers Presented at the Minisymposia Sessions of the Sixth World Congress on Computational Mechanics in conjunction with the Second Asian-Pacific Congress on Computational Mechanics, Z.H. Yao, M.W. Yuan and W.X. Zhong, editors, Tsinghua University Press Springer, 2004, p.212.
2. Y. Xu and J.J.W. van der Vegt, Space-time discontinuous Galerkin method for large amplitude nonlinear water waves, Computational Fluid Dynamics 2006: Proceedings of the Fourth International Conference on Computational Fluid Dynamics, ICCFD, Ghent, Belgium, July 10-14, 2006, H. Deconinck and E. Dick, (Eds.), Springer, 2009, pp. 53-58.
Preprint
1. C. Jin, Y. Xia and Y. Xu, Kernel compensation method forMaxwell eigenproblem with mimetic finite difference discretization and its preconditioners.
2. X. Cheng, J.J.W. van der Vegt, Y. Xu and H.J. Zwart, Discontinuous Galerkin Finite Element Methods for Linear Port-Hamiltonian Dynamical Systems.
3. L. Tian, Y. Xu, Y. Yang, J.J.W. van der Vegt, An energy stable local discontinuous Galerkin method for the isothermal Navier-Stokes-Korteweg equations.
4. J. Lu and Y. Xu, High order energy dissipative and conservative local discontinuous Galerkin methods for Camassa-Holm-Novikov equations.
5. J. Zhang, Y. Xia and Y. Xu, Well-balanced discontinuous Galerkin method with flux globalization for rotating shallow water equations.
6. L. Yao, Y. Xia and Y. Xu, High-order stabilization in the semi-implicit deferred correction methods.
Thesis
Y. Xu, Application of discrete functional analysis for Burgers-KdV equations (in Chinese), Master Degree Thesis, Tianjin Normal University, 2003.
Y. Xu, Local Discontinuous Galerkin Methods for Nonlinear Wave Equations, Ph.D Thesis, University of Science and Technology of China, 2005.