PUBLICATIONS

  1. C.A. Hall and X. Ye, Construction of Divergence Free Space for Incompressible Navier-Stokes Equation, J. Linear Algebra and Applications, Vol. 171 (1992) 9-52.

  2. X. Ye and C. A. Hall, Construction of an Optimal Weakly Divergence Free Macro Element, Int. J. Numerical Method for Engineering, Vol. 36 (1993) 2245-2262.

  3. G. Li, G. Anderson, X. Ye and K. Henle, Effects of Flow in Countercurrent Blood Vessels on the Temperature Distributions in Tissue During Rapid Hyperthermia, Advances in Bioheat and Mass Transfer.ASME 1993 WAM, HTD Vol. 268 (1993), 113-116

  4. X. Ye and G. Anderson, The Minimum Support Discrete Divergence Free Basis for a Mini Element, Applied Mathematics Letters, 6 (1993), 55-57.

  5. G. Anderson, X. Ye, K. Henle, Z. Yang and G. Li, A Numerical Study of Rapid heating for High Temperature Radio Frequency Hyperthermia, Int. J. Biomedical Computing, 35 (1994), 178-183.

  6. G. Anderson and X. Ye, An Numerical Analysis of a Focused Ultrasound Technique to Measure Perfusion, J. Biomechanical Engineering, 116 (1994), 178-183.

  7. X. Ye and C. Hall, The Construction of Null Basis for a Discrete Divergence Operator, J. Computational and Applied Mathematics, 58 (1995), 117-133.

  8. X. Ye. And G. Anderson, The Derivation of Minimal Support Basis Functions for a Discrete Divergence Operator, J. Computational and Applied Mathematics, 61 (1995), 105-116.

  9. P. Shi and X. Ye, A Least-Square Mixed Method for Stokes Equations, Numer. Methods for Partial Differential Equations, 13 (1997), 191-199.

  10. X. Ye and C. Hall, A Discrete Divergence Free Basis for Finite Element Methods, Numerical Algorithms, 16 (1997), 365-380.

  11. X. Ye, Domain Decomposition for A Least-Square Finite Element Method for the Stokes Equations, Applied Mathematics and Computation, 97 (1998), 45-53.

  12. W. Layton and X. Ye, Nonconforming Two-Level Discetization of Stream Function Form of the Navier-Stokes Equations, Applied Mathematics and Computation, 89 (1998), 173-183.

  13. Z. Cai, R. Parashkevov, T. Russell, and X. Ye, Overlapping domain decomposition for a mixed finite element method in three dimensions, In P. Bjorstad, M. Espedal, and D. Keyes (eds.) the 9th International Conference on Domain Decomposition Methods, Bergen, Norway, 1998, 188-196.

  14. X. Ye, Domain Decomposition for A Least-Square Finite Element Method for Second Order Elliptic Problem, Applied Mathematics and Computation, 91 (1998), 233-242.

  15. W. Layton and X. Ye, Two Level Discretizations of the Stream Functions Form of the Navier-Stokes Equations, Numerical Functional Analysis and Optimization, 20 (1999), 909-916.

  16. X. Ye, Two grid discretizations with backtracking of the stream function form of the Navier-Stokes equations, Applied Mathematics and Computation, 100 (1999), 131-138.

  17. J. Douglas, Jr., J.E. Santos, D. Sheen, and X.. Ye, Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems, Mathematical Modelling and Numerical Analysis, 33 (1999), 747-770.

  18. X. Ye, A Least Squares Finite Element Method for the Stokes Equations with improved Mass Balances, Computer; Mathematics with Applications, 38 (1999), 229-237.

  19. Z. Cai, X. Ye and H. Zhang, Least-Squares Finite Element Approximation for the Reissner-Mindlin Plate, J. Numer. Linear Algebra and Application, 6 (1999), 479-496.

  20. J. Douglas, Z. Cai and X. Ye, A Stable Quadrilateral nonconforming Element for the Navier-Stokes Equations, Calcolo, 36 (1999), 215-232.

  21. X. Ye, A Rectangular Element for the Reissner-Mindlin Plate, Numer. Method for PDE, 16 (2000), 184-193.

  22. Z. Cai and X. Ye, A Least-Squares Finite Element Approximation for the Compressible Stokes Equations, Numer. Method for PDE, 16 (2000), 62-70.

  23. X. Ye, Stabilized finite element approximations for the Reissner-Mindlin plate, Advances in Computational Mathematics, 13 (2000), 375-386.

  24. X. Ye, On the relationship between finite volume and finite element methods applied to the Stokes equations, Numer. Method for PDE, 17 (2001), 440-453.

  25. J. Wang and X. Ye, Superconvergence of finite element approximations for the Stokes problem by least squares surface fitting, SIAM J. Numer. Anal, 39 (2001), 1001-1013.

  26. X. Ye, Superconvergence of nonconforming finite element method for the Stokes equations, Numer. Method for PDE, 18 (2002), 143-154.

  27. X. Wang and X. Ye, Superconvergence analysis for the Navier-Stokes equations, Applied Numerical mathematics, 41 (2002), 515-527.

  28. X. Ye and C. Xu, A discontinuous Galerkin method for the Reissner-Mindlin plate in the primitive variables, Applied Mathematics and Computation, 149 (2003), 65-83.

  29. Z. Cai, R. R. Parashkevov, T. F. Russell and X. Ye, Domain decomposition for a mixed finite element method in three dimensions, SIAM J. Numerical Analysis. Anal., 41 (2003), 181-194.

  30. X. Ye, Discontinuous stable elements for incompressible flow, Advances in Computational Mathematics, 20 (2004), 333-345.

  31. J. Wang and X. Ye, A Superconvergent finite element scheme for the Reissner-Mindlin plate by projection methods, International Journal of Numeerical Analysis and Modeling, 1 (2004), 99-110.

  32. X. Ye, A new discontinuous finite volume method for elliptic problems, SIAM J. Numerical Analysis, 42 (2004), 1062-1072.

  33. Z. Cai and X. Ye, A mixed nonconforming finite element for linear elasticity, Numer. Method for PDE, 21 (2005), 1043-1051.

  34. X. Ye, A discontinuous finite volume method for the Stokes problem, SIAM J. Numerical Analysis, 44 (2006), 183-198.

  35. R. Lazarov and X. Ye, Stabilized discontinuous finite element approximations for Stokes equations, Journal of Computational and Applied Mathematics, 198 (2007), 236-252.

  36. J. Wang and X. Ye, New finite element methods in computational fluid dynamics by H(div}) elements, SIAM Numerical Analysis, 45 (2007), 1269-1286.

  37. S. Chou and X. Ye, Unified analysis of finite volume methods for second order elliptic problems, SIAM Numerical Analysis, 45 (2007), 1639-1653.

  38. S. Chou and X. Ye, Superconvergence of finite volume methods for the second order elliptic problem, Computer Methods in Applied Mechanics and Engineering, 196 (2007), 3706-3712.

  39. X. Ye, Analysis and convergence of finite volume method using discontinuous bilinear functions", Numerical Methods for Partial Differential Equations, 24 (2007), 335-348.

  40. J. Wang, X. Wang and X. Ye, Finite element methods for the Navier-Stokes equations by H(div) Elements, Journal of Computational Mathematics, 26, (2008), 410-436.

  41. M Cui and X. Ye, Superconvergence of finite volume methods for the Stokes equations, Numerical Methods for Partial Differential Equations, 25 (2009), 1212-1230.

  42. J. Wang, Y. Wang and X. Ye, A Robust Numerical Method for Stokes Equations Based on Divergence-free H(div) Finite Element Methods, SIAM J. Sci. Comput., 31 (2009), 2784-2802.

  43. J. Li, J. Wang and X. Ye, Superconvergence by $L^2$-projections for stabilized finite element methods for the Stokes equations, International Journal of Numerical Analysis and Modeling, 6 (2009), 711-723.

  44. X. Ye, A Posterior error estimate for finite volume methods of the second order elliptic problem, Numerical Methods for Partial Differential Equations, 7 (2011), 1156-1178.

  45. J. Wang, Y. Wang and X. Ye, A new finite volume method for the Stokes problems, International Journal of Numerical Analysis and Modeling, 7 (2010), 281-302.

  46. M. Cui and X. Ye, Unified analysis of finite volume methods for the Stokes equations, SIAM Numer. Anal., 48, (2010), 824-839.

  47. J. Wang, Y. Wang and X. Ye, A Posterior error estimate for the Stokes equations by H(div) elements, SIAM J. Sci, Comput., 33 (2011), 131-152.

  48. J. Wang, Y. Wang and X. Ye, A posteriori error estimate for stabilized finite element methods for the Stokes equations, International Journal of Numerical Analysis and Modeling, 9 (2012), 1-16.

  49. J. Liu, L. Mu and X. Ye, A Comparative Study of Locally Conservative Numerical Methods for Darcy flow, Procedia Computer Science, 00 (2011), 1-10.

  50. J. Liu, L. Mu and X. Ye, Adaptive discontinuous finite volume methods for the second order elliptic problem, Journal of Computational and Applied Mathematics, 235 (2011), 5422-5431.

  51. Z. Cai, S. Zhang and X. Ye, Recovery-based error estimators for interface problems: discontinuous Galerkin finite elements, SIAM J. Numer. Anal, 49 (2011), 1761-1781.

  52. Lin Mu and X. Ye, Finite volume method for the Navier-Stokes equations, Nonlinear Analysis: Theory, Methods & Applications, 74 (2011), 6686-6695

  53. J. Liu, L. Mu and X. Ye, L2 error estimation for DGFEM for elliptic problems with low regularity, Applied Mathematics Letters, 25 (2012) 1614-1618.

  54. J. Liu, L. Mu, R. Jari and X. Ye, Convergence of the discontinuous finite volume method for elliptic problems with minimum regularity, Journal of Computational and Applied Mathematics, 236 (2012), 4537-4546.

  55. J. Wang, Y. Wang and X. Ye, A posteriori error estimate for stabilized finite element methods for the Stokes equations, International Journal of Numerical Analysis and Modeling, 9 (2012) 1-16.

  56. J. Wang, Y. Wang and X. Ye, A posterior error estimate for finite volume methods for the Stokes Equations, Mathematical Methods in the Applied Sciences, (2012), accepted.

  57. T. Lin and X. Ye, A posteriori error estimate for finite volume methods of a second order elliptic equation with bilinear trial functions, Journal of Computational and Applied Mathematics, 254 (2013), 185-191.

  58. J. Wang, Y. Wang and X. Ye, Unified a posteriori error estimator for finite element methods for the Stokes equations, International Journal of Numerical Analysis and Modeling, 10 (2013), 551-570.

  59. L. Mu, J. Wang, Y. Wang and X. Ye, A computational study of the weak Galerkin method for the second order elliptic equations, Numerical Algorithm, 63, (2013) 753-777.

  60. J. Wang and X. Ye, A weak Galerkin method for second order elliptic problems, Journal of Computational and Applied Mathematics, 241 (2013), 103-115.

  61. L. Mu, J. Wang, Y. Wang and X. Ye, A weak Galerkin mixed finite element method for biharmonic equations, Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications, 45 (2013), 247-277.

  62. L. Mu, J. Wang, G. Wei, X. Ye and S. Zhao, Weak Galerkin method for the elliptic interface problem, J. of Computational Physics, 250 (2013), 106-125.

  63. L. Mu, J. Wang, Y. Wang and X. Ye, Interior penalty discontinuous Galerkin method on very general polygonal and polyhedral meshes, Journal of Computational and Applied Mathematics, 255 (2014), 432-440.

  64. J. Wang and X. Ye, A Weak Galerkin mixed finite element method for second-order elliptic problems, Math. Comp., 83 (2014), 2101-2126.

  65. L. Chen, J. Wang and X. Ye, A posteriori error estimates for Weak Galerkin finite element methods for second order elliptic problem, J. of Scientific Computing, 59 (2014), 496-511.

  66. L. Mu, J. Wang, X. Ye, S. Zhang, $C^0$ Weak Galerkin finite element methods for the biharmonic equation, J. of Scientific Computing, 59 (2014), 437-495.

  67. L. Mu, J. Wang, X. Ye and S. Zhao, Numerical studies on the Weak Galerkin method for the Helmholtz equation with large wave number, Communications in Computational Physics, 15 (2014), 1461-1479.

  68. L. Mu, J. Wang, and X. Ye, A weak Galerkin finite element method for biharmonic equations on polytopal meshes, Numerical Methods for Partial Differential Equations, 30 (2014), 1003-1029.

  69. L. Mu, J. Wang and X. Ye, Weak Galerkin finite element method for the Helmholtz equation with large wave number on polytopal meshes, IMA Journal of Numerical Analysis, 2014, (DOI) 10.1093/imanum/dru026.

  70. L. Mu, J. Wang, and X. Ye, A stable numerical algorithm for the Brinkman equations by weak Galerkin finite element methods, J. of Computational Physics, 273 (2014), 327-342.

  71. G. Lin, J. Liu, L.Mu and X. Ye, Weak Galerkin finite element methods for Darcy flow: Anisotropy and heterogeneity, J. of Computational Physics, 276 (2014), 422-437.

  72. L. Mu, X. Wang and X. Ye, A Modified Weak Galerkin Finite Element Method for the Stokes Equations, Journal of Computational and Applied Mathematics, 275 (2015), 79-90.

  73. L. Mu, J. Wang, and X. Ye, Weak Galerkin finite element method for second-order elliptic problems on polytopal meshes, International Journal of Numerical Analysis and Modeling, 12 (2015), 31-53.

  74. L. Mu, J. Wang, X. Ye and S. Zhang, A weak Galerkin finite element method for the Maxwell equations, J. of Scientific Computing, to appear.



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