PUBLICATIONS: SUBJECT CLASSIFICATION

A POSTERIORI ERROR ANALYSIS AND ADAPTIVITY
  • General interests

  • Free boundary and phase transition

  • Convection-dominated diffusion

  • Electromagnetism

    • MULTISCALE COMPUTATION OF FLOW TRANSPORT IN HETEROGENEOUS POROUS MEDIA

    MATHEMATICAL AND NUMERICAL ANALYSIS FOR FREE BOUNDARY PROBLEMS

  • Superconductivity

  • Continuous casting

  • Phase transitions

    • MISCELLANEOUS

    A POSTERIORI ERROR ANALYSIS AND ADAPTIVITY

    General interests

    1. The adaptive immersed interface finite element method for elliptic and Maxwell interface problems, with Yuanming Xiao and Linbo Zhang, Journal of Computational Physics 228 (2009), 5000-5019.

    2. Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems,
      with H. Wu, Science in China: Series A Mathematics 49 (2006), 1405-1429.

    3. An adaptive finite element method with reliable and efficient error control for linear parabolic problems,
      with F. Jia, Math. Comp. 73 (2004), 1163-1197.

    4. On the efficiency of adaptive finite element methods for elliptic problems with discontinous coefficients,
      with S. Dai, SIAM J. Sci. Comput. 24 (2002), 443-462.

    Free boundary and phase transitions

    1. Adaptive Galerkin method with error control for a dynamical Ginzburg-Landau model in superconductivity,
      with S. Dai, SIAM J. Numer. Anal. 38 (2001), 1961-1985.

    2. A posteriori error control and adaptivity for a phase relaxation model,
      with R.H. Nochetto and A. Schmidt, Math. Model. Numer. Anal. 34 (2000), 775-797.

    3. An adaptive finite element method with error control for the continuous casting problem,
      with R.H. Nochetto and A. Schmidt, Computer Meth. Appl. Mech. Engrg. 189 (2000), 249-276

    4. Residual type a posteriori error estimates for elliptic obstacle problems,
      with R.H. Nochetto, Numer. Math. 84 (2000), 527-548

    Convection-dominated diffusion

    1. Sharp $L^1$ a posteriori error analysis for nonlinear convection-diffusion problems with G.H. Ji, Math. Comp. 75 (2006), 43-71.

    2. Adaptive computation for convection dominated diffusion problems,
      with G.H. Ji, Science in China (Series A) 47 (2004), Supp. 22-31.

    3. An adaptive finite element method with error control for the continuous casting problem,
      with R.H. Nochetto and A. Schmidt, Computer Meth. Appl. Mech. Engrg. 189 (2000), 249-276

    Electromagnetism

    1. An Adaptive Finite Element Method for the Eddy Current Model with Circuit/Field Couplings with Junqing Chen, Tao Cui and Linbo Zhang, SIAM J. Sci. Computing, to appear.

    2. The adaptive immersed interface finite element method for elliptic and Maxwell interface problems, with Yuanming Xiao and Linbo Zhang, Journal of Computational Physics 228 (2009), 5000-5019.

    3. An $hp$ Adaptive Uniaxial Perfectly Matched Layer Method for Helmholtz Scattering Problems with B.Q. Guo and Y.M. Xiao, Communications in Computational Physics 5 (2009), 546-564.

    4. Convergence of the time-domain perfectly matched layer method for acoustic problems International Journal of Numerical Analysis and Modeling, 6 (2009), 124-146.

    5. On Maxwell Equations with the transparent boundary condition with J.-C. Nedelec, J. Comput. Math. 26 (2008), 284-296.

    6. An adaptive uniaxial perfectly matched layer technique for Time-Harmonic Scattering Problems with X.M. Wu, Numerical Mathematics: Theory, Methods and Applications, 1 (2008), 113-137.

    7. An adaptive perfectly matched layer technique for 3-D time-harmonic electromagnetic scattering problems with J. Chen, Math. Comp. 77 (2008), 673-698.

    8. An adaptive multilevel method for time-harmonic Maxwell equations with singularities,
      with L. Wang and W. Zheng, SIAM J. Sci. Comput., 29 (2007), 118-138.

    9. An adaptive finite element method for the ${\bf H}-\psi$ formulation of time-dependent eddy current problems,
      with W.Y. Zheng and L. Wang, Numer. Math. 103 (2006), 667-689.

    10. An Adaptive Perfectly Matched Layer Technique for Time-harmonic Scattering Problems,
      with X.Z. Liu, SIAM J. Numer. Anal. 43 (2005), 645-671.

    11. An adaptive finite element method for diffraction gratings,
      with G. Bao and H.J. Wu, Journal of the Optical Society of America A, 22 (2005), 1106-1114.

    12. An Adaptive Finite Element Method with Perfectly Matched Absorbing Layers for the Wave Scattering by Periodic Structures,
      with H.J. Wu, SIAM J. Numer. Anal. 41 (2003), 799-826.

    13. Finite element methods with matching and non-matching meshes for Maxwell equations with discontinuous coefficients,
      with Q. Du and J. Zou, SIAM J. Numer. Anal. 37 (2000), 1524-1570

    MULTISCALE COMPUTATION OF FLOW TRANSPORT IN HETEROGENEOUS POROUS MEDIA

    1. Upscaling of a class of nonlinear parabolic equations for the flow transport in heterogeneous porous media,
      with W.B. Deng and H. Ye, Communications in Mathematical Sciences 3 (2005), 493-515.

    2. A new upscaling method for the solute transport equations,
      with W.B. Deng and H. Ye, Continuous and Discrete Dynamical Systems 13 (2005), 941-962.

    3. Numerical homogenization of well singularities in the flow transport through heterogeneous porous media,
      with X.Y. Yue, Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 1 (2003), 260-303.

    4. A mixed multiscale finite element method for elliptic problems with oscillating coefficients,
      with T.Y. Hou, Math. Comp. 72 (2002), 541-576.

    MATHEMATICAL AND NUMERICAL ANALYSIS FOR FREE BOUNDARY PROBLEMS

    Superconductivity

    1. Adaptive Galerkin method with error control for a dynamical Ginzburg-Landau model in superconductivity,
      with S. Dai, SIAM J. Numer. Anal. 38 (2001), 1961-1985.

    2. An upwinding finite element method for a mean field model for superconducting vortices,
      with Q. Du, Math. Model. Numer. Anal. 34 (2000), 687-706.

    3. Numerical solutions of an optimal control problem governed by a Ginzburg-Landau model in superconductivity,
      with K.-H. Hoffmann, Numer. Funct. Anal. Optimiz. 19 (1998), 737-758.

    4. Justification of a two-dimensional evolutionary Ginzburg-Landau superconductivity model,
      with C.M. Elliott and Q. Tang, RAIRO Math. Model. Numer. Anal. 32 (1998), 25-50.

    5. Global classical solutions to a non-isothermal dynamical Ginzburg-Landau model in superconductivity,
      with K.-H. Hoffmann, Numer. Funct. Anal. Optimiz. 18 (1997), 901-920.

    6. On the Lawrence-Doniach model for layered superconductors,
      with K.-H. Hoffmann and L. Jiang, Euro. J. Appl. Math. 8 (1997), 369-387.

    7. Mixed finite element methods for a dynamical Ginzburg-Landau model in superconductivity,
      Numer. Math. 76 (1997), 323-353.

    8. Modelling and numerical solutions of a gauge periodic time dependent Ginzburg-Landau model for type-II superconductors,
      J. Comput. Math. 15 (1997) 365-384.

    9. Optimal control of dynamical Ginzburg-Landau vortices in Superconductivity,
      with K.-H. Hoffmann, Numer. Funct. Anal. Optimiz. 17 (1996), 241-258.

    10. Numerical Studies of a non-stationary Ginzburg-Landau model for superconductivity,
      with K.-H. Hoffmann, Adv. Math. Sci. Appl. 5 (1995), 363-389.

    Continuous casting

    1. An adaptive finite element method with error control for the continuous casting problem,
      with R.H. Nochetto and A. Schmidt, Computer Meth. Appl. Mech. Engrg. 189 (2000), 249-276.

    2. Numerical methods for Stefan problems with prescribed convection and nonlinear flux,
      with T.M. Shih and Y.X.Yue, IMA J. Numer. Anal. 20 (2000), 81-98.

    3. Approximation of a two-phase continuous casting Stefan problems,
      with L. Jiang, J. Partial Differential Equations 11 (1998), 59-72.

    Phase transitions

    1. A posteriori error control and adaptivity for a phase relaxation model,
      with R.H. Nochetto and A. Schmidt, Math. Model. Numer. Anal. 34 (2000), 775-797.

    2. Asymptotic behaviors of Landau-Devonshire-Ginzburg model for structural phase transitions in shape memory alloys,
      with K.-H. Hoffmann, Adv. Math. Sci. Appl. 4 (1994), 209-226.

    3. On a one-dimensional nonlinear thermoviscoelastic model for structural phase transitions in shape memory alloys,
      with K.-H. Hoffmann, J. Diff. Equations 112 (1994), 325-350.

    4. An error estimate for a finite element scheme for a phase field model,
      with K.-H. Hoffmann, IMA J. Numer. Anal. 14 (1994), 243-255.

    5. Optimal boundary controls for a phase field model,
      IMA J. Math. Contr. Inform. 10 (1993), 157-176.

    MISCELLANEOUS

    1. Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems,
      with H. Wu, Science in China: Series A Mathematics, to appear.

    2. On the efficiency of adaptive finite element methods for elliptic problems with discontinous coefficients,
      with S. Dai, SIAM J. Sci. Comput. 24 (2002), 443-462.

    3. On the augmented Lagrangian approach to Signorini elastic contact problem,
      Numer. Math. 88 (2001), 641-659.

    4. An augmented Lagrangian method for identifying discontinuous parameters in elliptic systems,
      with J. Zou, SIAM J. Control and Optimization 37 (1999), 892-910.

    5. Finite element methods and their convergence for elliptic and parabolic interface problems,
      with J. Zou, Numer. Math. 79 (1998), 175-202.

    6. A full-discretization moving FEM with optimal convergence rate,
      with G.P. Liang, Chinese J. Num. Math. \& Appl. 12 (1990), 91-111.