Publications
- X. Xu, X. Zhang, W. Zheng, Modelling and Efficient Numerical Method for Ion Transports in Liquids under Electromagnetic Influence, submitted.
- X. Xu, A theoretical framework for a moving grid finite element method, submitted.
- S. Xiao, X. Xu, A moving mesh method for porous medium equation
by the Onsager variational principle, submitted
Refereed Journal Papers
- Y. Zhang, X. Gu, Y. Wang, X. Xu, L. Zhang, Solution landscape of droplet on rough surfaces: wetting transition and directional
transport, to appear in Soft Matter.
- 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.
- 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)
- Y. Liu, X. Xu, A variational discretization method for mean curvature flows by
the Onsager principle, CSIAM Trans. Appl. Math. 6, 63-95,
(2025)
- H. Chen, H. Liu ,X. Xu, The Onsager principle and structure preserving numerical schemes, J. Comput. Phys. 523,
113679, (2025)
- T. Tang, X. Xu, Transformed model reduction for partial differential equations with sharp inner layers
, SIAM J. Sci. Comput. 46, A2178--A2201, (2024)
- 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).
- S. Lu, X. Xu, Numerical Investigations on Trace finite element methods for the Laplace-Beltrami eigenvalue problem , J. Sci. Comput. 97:12, (2023).
- S. Xiao, X. Xu, Z, Zhang Multiscale analysis for dynamic contact angle hysteresis on rough surfaces, SIAM Mult. Model. Simul. 21, 400-425 (2023).
- X. Xu, A variational analysis for the moving finite element method for gradient flows, J. Comput. Math. 41, 191-210 (2023).
- M. Doi, X. Xu, Diffusion limited escape rate of a complex molecule in muti-dimensional confinement,J. Phys. Chem. B. 33, 6771-6179 (2022).
- Z. Zhang, X. Xu, Effective boundary conditions for dynamic contact angle hysteresis on chemically
inhomogeneous surfaces, J. Fluid Mech. vol. 935, A34 (2022).
- Y. Chen, X. Xu Dynamics of droplets on general surfaces with curvature gradient, Phys. Fluids. 33, 082107 (2021).
- S. Lu, X. Xu, An efficient diffusion generated motion method for wetting dynamics, J. Comput. Phys., 441, 110476 (2021).
- M. Olshanskii, X. Xu, V. Yushutin, A finite element method for Allen-Cahn equation on deforming surface, Computers & Math. Appl. 90, 148-158 (2021).
- X. Xu, W.J. Ying, An adaptive threshold dynamics method for three-dimensional
wetting on rough surfaces , Comm. Comput. Phys., 29, 57-79 (2021).
- X. Xu, X.P. Wang, Theoretical analysis for dynamic contact angle hysteresis on
chemically patterned surfaces, Phys. Fluids. 32, 112102 (2020). (Editor's Pick)
- 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).
- X. Xu, C. Calderer, M. Doi, D. Henao, Debonding waves in gel thin films , Proc. Royal Soc. A. 476, 20200001., (2020).
- 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).
- 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)
- D. Wang, X.P. Wang, X. Xu, An improved threshold dynamics method for wetting dynamics,J. Comput. Phys. 392, 291-310, (2019)
- 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).
- 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).
- 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).
- 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).
- 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).
- M. Olshanskii, X. Xu, A trace finite element method for PDEs on evolving surfaces, SIAM J. Sci. Comput., Vol 39, A1301-A1319, (2017).
- 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).
- X. Xu, D. Wang, X.P. Wang, A thresholding method for wetting problem on rough surface, J. Comput. Phys.,Vol 330, 510-528, (2017).
- 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).
- X. Xu, Modified Wenzel and Cassie equation for wetting on rough surfaces, SIAM J. Appl. Math. Vol 76, 2353-2374, (2016).
- 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).
- 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).
- X. Xu, Y.N. Di, M. Doi, Variational method for contact line problems in sliding liquids, Phys. Fluids, Vol 28, 087101 (2016).
- 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).
- 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).
- 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).
- X. Xu and X.P. Wang, Non-Darcy behavior in two-phase channel flow, Phys. Rev. E 90, 023010 (2014)
- 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)
- 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).
- 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).
- X. Xu and X.P. Wang, The modified Cassie's equation and contact angle hysteresis, Colloid and Polymer Science, 291 , 299-306(2013).
- X. Chen, X.P. Wang, X. Xu, Effective contact angle for rough boundary, Physica D: Nonlinear Phenomena 242 (1), 54-64(2013).
- M. Olshanskii, A. Reusken, X. Xu, On surface meshes induced by level set functions, Comput. Visual. Sci., Vol. 15 53-60 (2012).
- 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).
- X. Xu, D. Henao, An efficient numerical method for cavitation in nonlinear elasticity, Math. Mod. Meth. Appl. Sci. Vol. 21, 1733-1760 (2011).
- 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).
- Z. Li, X. Xu, Convergence and stability of a numerical method for micromagnetics, Numer. Math. Vol. 112, 245-265 (2009).
- 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).
- 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
- X. Xu, Y. Di, M. Doi, Using Onsager principle as an approximation tool for complicated two-phase tow problems, Proceeding of ICCM 2019.
- M. Olshanskii, A. Reusken, X. Xu, A volume mesh finite element method for PDEs on surfaces, Proceeding of ECCOMAS 2012.
Invited Book Chapter
- 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
- W. Jiang, X. Xu, W. Bao, D. Srolovitz, Power-law scaling for solid-state dewetting of thin films:
an Onsager variational approach.