Publications

  1. Z. Qiao, X. Xu, X. Yang, Y. Zhang A unified variational framework and lattice Boltzmann method for non-isothermal two-phase flows with phase transitions and wetting effects, submitted.
  2. R. Guo, J. Shen, S. Xu, X. Xu, Phase-field modeling and energy-stable schemes for osmotic flow through semi-permeable membrane, submitted.
  3. X. Xu, A theoretical framework for a moving grid finite element method, submitted.
Refereed Journal Papers
  1. X. Xu, X. Zhang, W. Zheng, Modelling and efficient numerical method for ion transports in liquids under electromagnetic influence, to appear in J. Comput. Phys.
  2. D. Wang, X. Xu, B. Zou, Deep learning methods for singular variational problems with Lavrentiev phenomena , to appear in Comm. Comput. Phys.
  3. M.R. Lv, B.Z. Lu, X. Xu, The effect of oscillating electric field on the solution of the Poisson-Nernst-Planck Equations: Multiscale analysis and numerical simulations, (in Chinese) to appear in J. Numer. Meth. Computer Appl.
  4. S. Xiao, X. Xu, A moving mesh method for porous medium equation by the Onsager variational principle, J. Comput. Phys. 536, 114061 (2025)
  5. Y. Zhang, X. Gu, Y. Wang, X. Xu, L. Zhang, Solution landscape of droplet on rough surfaces: wetting transition and directional transport, Soft Matter 21 2729-2737 (2025).
  6. S. Lu, X. Xu, A narrow band numerical method for a surface reaction-diffusion system coupled with surface motion, J. Sci. Comput., 103:2, (2025)
  7. Y. Liu, X. Xu, A variational discretization method for mean curvature flows by the Onsager principle, CSIAM Trans. Appl. Math. 6, 63-95, (2025)
  8. H. Chen, H. Liu ,X. Xu, The Onsager principle and structure preserving numerical schemes, J. Comput. Phys. 523, 113679, (2025)
  9. T. Tang, X. Xu, Transformed model reduction for partial differential equations with sharp inner layers , SIAM J. Sci. Comput. 46, A2178--A2201, (2024)
  10. X. Xu, A unified variational framework on macroscopic computations for two-phase flow with moving contact lines , SIAM J. Sci. Comput. 45, B776-B801, (2023).
  11. S. Lu, X. Xu, Numerical Investigations on Trace finite element methods for the Laplace-Beltrami eigenvalue problem , J. Sci. Comput. 97:12, (2023).
  12. S. Xiao, X. Xu, Z, Zhang Multiscale analysis for dynamic contact angle hysteresis on rough surfaces, SIAM Mult. Model. Simul. 21, 400-425 (2023).
  13. X. Xu, A variational analysis for the moving finite element method for gradient flows, J. Comput. Math. 41, 191-210 (2023).
  14. M. Doi, X. Xu, Diffusion limited escape rate of a complex molecule in muti-dimensional confinement,J. Phys. Chem. B. 33, 6771-6179 (2022).
  15. Z. Zhang, X. Xu, Effective boundary conditions for dynamic contact angle hysteresis on chemically inhomogeneous surfaces, J. Fluid Mech. vol. 935, A34 (2022).
  16. Y. Chen, X. Xu Dynamics of droplets on general surfaces with curvature gradient, Phys. Fluids. 33, 082107 (2021).
  17. S. Lu, X. Xu, An efficient diffusion generated motion method for wetting dynamics, J. Comput. Phys., 441, 110476 (2021).
  18. M. Olshanskii, X. Xu, V. Yushutin, A finite element method for Allen-Cahn equation on deforming surface, Computers & Math. Appl. 90, 148-158 (2021).
  19. X. Xu, W.J. Ying, An adaptive threshold dynamics method for three-dimensional wetting on rough surfaces , Comm. Comput. Phys., 29, 57-79 (2021).
  20. X. Xu, X.P. Wang, Theoretical analysis for dynamic contact angle hysteresis on chemically patterned surfaces, Phys. Fluids. 32, 112102 (2020). (Editor's Pick)
  21. X. Xu, M. Doi, J. Zhou, Y. Di, Theoretical analysis for flattening of a rising bubble in a Hele-Shaw cell, Phys. Fluids. 32, 092102, (2020).
  22. X. Xu, C. Calderer, M. Doi, D. Henao, Debonding waves in gel thin films , Proc. Royal Soc. A. 476, 20200001., (2020).
  23. X. Xu, Y. Zhao, X.P. Wang, Analysis for contact angle hysteresis on rough surfaces by a phase-field model with a relaxed boundary condition, SIAM J. Appl. Math. 79, 2551-2568, (2019).
  24. M. Doi, J. Zhou, Y. Di, X. Xu, Application of Onsager Machlup integral in solving dynamic equations in non-equilibrium systems , Phys. Rev. E 99 (6), 063303, (2019)
  25. D. Wang, X.P. Wang, X. Xu, An improved threshold dynamics method for wetting dynamics,J. Comput. Phys. 392, 291-310, (2019)
  26. S. Guo, X. Xu, T. Qian, Y. Di, M. Doi, P. Tong, Onset of thin film meniscus along a fiber, J. Fluid Mech. Vol 865, 650-680, (2019).
  27. X. Xu, Y.N. Di, H. Yu, Sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact lines , J. Fluid Mech.,Vol 849, 805-833, (2018).
  28. C. Lehrenfeld, M. Olshanskii, X. Xu, A stabilized trace finite element method for partial differential equations on evolving surfaces , SIAM J. Numer. Anal., Vol 56, 1643-1672 (2018).
  29. Y.N. Di, X. Xu, J. Zhou, M. Doi, Analysis of thin film dynamics in coating problems using Onsager principle , Chinese Physics B, Vol 27, 024501 (2018).
  30. X. Xu, X.P. Wang, Mathematical Analysis for Wetting on Rough Surface(in Chinese, Dedicated to 90th Birthday of Prof. Min Qian), Science China: Mathematics, Vol. 47, 1771-1786 (2017).
  31. M. Olshanskii, X. Xu, A trace finite element method for PDEs on evolving surfaces, SIAM J. Sci. Comput., Vol 39, A1301-A1319, (2017).
  32. A. Reusken, X. Xu, L. Zhang, Finite element methods for a class of continuum models for immiscible flows with moving contact lines, Int. J. Numer. Meth. Fluids, Vol 84, 268-291, (2017).
  33. X. Xu, D. Wang, X.P. Wang, A thresholding method for wetting problem on rough surface, J. Comput. Phys.,Vol 330, 510-528, (2017).
  34. X. P. Wang, X. Xu, A dynamic theory for contact angle hysteresis on chemically rough boundary, Disc. Cont. Dynam. Syst. A, Vol. 37,1061-1073 (2017).
  35. X. Xu, Modified Wenzel and Cassie equation for wetting on rough surfaces, SIAM J. Appl. Math. Vol 76, 2353-2374, (2016).
  36. P. Ming, X. Xu, A multiscale finite element method for oscillating Neumann problem on rough domain SIAM Mult. Model. Simul., Vol 14,1276-1300, (2016).
  37. X. Xu, Analysis for Wetting on Rough Surfaces by a Three-dimensional Phase Field Model, Disc. Cont. Dynam. Syst. B.,Vol 21,2839-2850 (2016).
  38. X. Xu, Y.N. Di, M. Doi, Variational method for contact line problems in sliding liquids, Phys. Fluids, Vol 28, 087101 (2016).
  39. Y.N. Di, X. Xu, M. Doi, Theoretical Analysis for Meniscus Rise of a Liquid Contained between a Flexible Film and a Solid Wall, Euro. Phys. Lett. 113, 36001 (2016).
  40. D. Henao, C. Mora-Corral, X. Xu, A numerical study of void coalescence and fracture in nonlinear elasticity, Comput. Meth. Appl. Mech. Engrg., Vol. 303, 163-184 (2016).
  41. D. Henao, C. Mora-Corral, X. Xu, Gamma-Convergence approximation of fracture and cavitation in nonlinear elasticity, Arch. Rational Mech. Anal., Vol. 216, 813-879, (2015).
  42. X. Xu and X.P. Wang, Non-Darcy behavior in two-phase channel flow, Phys. Rev. E 90, 023010 (2014)
  43. M. Olshanskii, A. Reusken and X. Xu, An Eulerian space-time finite element method for diffusion problems on evolving surfaces, SIAM J. Numer. Anal., Vol 52, 1354-1377 (2014)
  44. X. Chen, X.P.Wang, X. Xu, Analysis of the Cahn-Hilliard equation with relaxation boundary condition modelling contact angle,, Arch. Rational Mech. Anal., Vol. 213 1-24 (2014).
  45. M. Olshanskii, A. Reusken, X. Xu, A stabilized finite element method for advection-diffusion equations on surfaces, IMA J. Numer. Math., Vol. 34 732-758 (2014).
  46. X. Xu and X.P. Wang, The modified Cassie's equation and contact angle hysteresis, Colloid and Polymer Science, 291 , 299-306(2013).
  47. X. Chen, X.P. Wang, X. Xu, Effective contact angle for rough boundary, Physica D: Nonlinear Phenomena 242 (1), 54-64(2013).
  48. M. Olshanskii, A. Reusken, X. Xu, On surface meshes induced by level set functions, Comput. Visual. Sci., Vol. 15 53-60 (2012).
  49. X. Xu and X.P. Wang, Analysis of wetting and contact angle hysteresis on chemically patterned surfaces, SIAM J. Appl. Math. Vol. 71, 1753-1779 (2011).
  50. X. Xu, D. Henao, An efficient numerical method for cavitation in nonlinear elasticity, Math. Mod. Meth. Appl. Sci. Vol. 21, 1733-1760 (2011).
  51. X. Xu and X.P. Wang, Derivation of the Wenzel and Cassie Equations from a Phase Field Model for Two Phase Flow on Rough Surface, SIAM J. Appl. Math. 70, 2929-2941 (2010).
  52. Z. Li, X. Xu, Convergence and stability of a numerical method for micromagnetics, Numer. Math. Vol. 112, 245-265 (2009).
  53. X. Xu, Z. Li, Non-conforming finite element and artificial boundary in multi-atomic Young measure approximation for micromagnetics, Appl. Numer. Math. 59, 920- 937 (2009).
  54. X. Xu, Z. Li, A posteriori error estimates of a non-conforming finite element method for problems with artificial boundary conditions, J. Comp. Math. 27, 677-696 (2009).
Refereed Conference Paper
  1. X. Xu, Y. Di, M. Doi, Using Onsager principle as an approximation tool for complicated two-phase tow problems, Proceeding of ICCM 2019.
  2. M. Olshanskii, A. Reusken, X. Xu, A volume mesh finite element method for PDEs on surfaces, Proceeding of ECCOMAS 2012.
Invited Book Chapter
  1. X. Xu, X.P. Wang, Recent mathematical analysis of contact angle hysteresis, "Advances in Contact Angle, Wettability and Adhesion", Vol 2, 2015, edited by K. Mittal.
Preprint
  1. W. Jiang, X. Xu, W. Bao, D. Srolovitz, Power-law scaling for solid-state dewetting of thin films: an Onsager variational approach.