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徐岩

Professor

Supervisor of Doctorate Candidates

Supervisor of Master's Candidates


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Administrative Position:Professor

Contact Information:E-mail: yxu@ustc.edu.cn

Other Post:测试测试

Alma Mater:University of Science and Technology of China

Discipline:Mathematics

Academic Honor:

2009   Participant of the Program for New Century Excellent Talents of Ministry of Education of China

2017   National outstanding youth fund winner

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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 Mathematics22 (2004), pp.250-274.

3.   Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for nonlinear Schrodinger equations Journal of Computational Physics205 (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 Mathematics22(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 D208 (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 equationsComputer 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 wavesJournal of Computational Physics, 224 (2007), pp.17-39.

9.   Y. Xia, Y. Xu and C.-W. Shu, Efficient time discretization for local discontinuous Galerkin methodsDiscrete and Continuous Dynamical Systems - Series B(2007), pp. 677-693.

10.  Y. Xia, Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for the Cahn-Hilliard type equationsJournal of Computational Physics,  227 (2007), pp. 472-491.

11.  Y. Xu and C.-W. Shu, A local discontinuous Galerkin method for the Camassa-Holm equationSIAM Journal on Numerical Analysis46 (2008), pp.1998-2021.

12.  Y. Xu, J.J.W. van der Vegt and O. Bokhove, Discontinuous Hamiltonian finite element method for linear hyperbolic systemsJournal 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 limitSIAM 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 systemCommunications 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 graphsJournal 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 equationsCommunications 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 systemJournal 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 meshesInternational 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 equationCommunications 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 equationsSIAM 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 meshesJournal 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 equationChinese 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-dimensionsMathematics of Computation, 81(2012), pp.1929-1950.

25.  L. Ji, Y. Xu and J.K. Ryan, Negative order norm estimates for nonlinear hyperbolic conservation lawsJournal 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 materialCommunications 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 equationsJournal 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 barJournal 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 phenomenaCommunications in Computational Physics, 15(2014), pp. 1012-1028.

30.  Y. Xia and Y. Xu, Conservative local discontinuous Galerkin methods for the Schoedinger-KdV systemCommunications 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 systemJournal 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 fluidsJournal 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 SurfacesCommunications 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 equationsCommunications 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 equationJournal 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 systemJournal 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 ElastographyUltrasonic 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 operatorJournal 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 SurfacesCommunications 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 simulationJournal 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 equationSIAM 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 equationsJournal 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 crystalsJournal 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 equationsJournal of Computational Physics, 338(2017), pp.269-284.

47.  F. Zhang, Y. Xu, F. Chen, Discontinuous Galerkin Based Isogeometric Analysis for Geometric flowsJournal 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 equationsJournal 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 equationCommunications 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 equationsJournal of Scientific Computing, 77(2018), pp.1001-1029.

52.  T. Ma and Y. Xu, Local discontinuous Galerkin methods for the two-dimensional Camassa-Holm equationCommunications 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 equationsJournal 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 problemsCommunications 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 DerivativesJournal 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 flowsCommunications 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 equationsJournal 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 discretizationsSIAM 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 EquationsSIAM 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 methodsSIAM 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 EquationJournal 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 derivativesMathematics 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 equationsJournal 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 equationsJournal 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 equationsCommunications 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 plateAdvances 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 mobilityComputational 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 equationsJournal 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 equationsCommunications 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 equationsAdvances in Aerodynamics, 4(2022), Article number: 22.

74.  X. Yu, Y. Xu, Q. Du, Asymptotically compatible approximations of linear nonlocal conservation laws with variable horizonNumerical 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 interactionsJournal of Scientific Computing, 92(2022), Article number: 59.

76.  Z. Lu and Y. Xu, A parallel eigensolver for photonic crystals discretized by edge finite elementsJournal 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 equationsJournal 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 equationsJournal 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 equationNumerical 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 fieldsComputers 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 systemJournal of Computational and Applied Mathematics, 436 (2024), Article number: 115416.

84.  F. Yan, J.J.W. van der Vegt, Y. Xia and Y. XuEntropy dissipative higher order accurate positivity preserving time-implicit discretizations for nonlinear degenerate parabolic equationsJournal 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 surfaceJournal of Geometry and Physics197(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 modelsCommunications on Applied Mathematics and Computation, 6(2024), pp.372-398.

89.    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.

90.   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.

91.  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.

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.    W. Zheng and Y. Xu,  Invariants preserving time-implicit local discontinuous Galerkin schemes for high-order nonlinear wave equations.

2.  X. Meng, Y. Xu and J.J.W. van der Vegt,  Energy conservative local discontinuous Galerkin methods for the Euler-Korteweg equations.

3.      J. Zhang, Y. Xia and Y. Xu, Equilliburm preserving space in discontinuous Galerkin methods for hyperbolic balance laws.

4.   C. Jin, Y. Xia and Y. Xu, Kernel compensation method forMaxwell eigenproblem with mimetic finite difference discretization and its preconditioners.

5.  Y. W u and Y. Xu, A High-Order Local Discontinuous Galerkin Method for the p-Laplace Equation .

6.    J. Zhang, Y. Xia and Y. Xu, Well-balanced path-conservative discontinuous Galerkin methods with equilibrium preserving space  for two-layer shallow water equations.

7. 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.

8. 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.

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.