Journal Publications

  1. Jing Wang, Xu Zhang, Qiao Zhuang.
    An Immersed Crouzeix-Raviart Finite Element Method for Navier-Stokes Interface Problems.
    International Journal of Numerical Analysis & Modeling, 19 (2022), no.4, 563-586. []
  2. David Lund, Xiaoming He, Xu Zhang, Daoru Han.
    Weak scaling of the parallel immersed-finite-element particle-in-cell (PIFE-PIC) framework with lunar plasma charging simulations.
    Computational Particle Mechanics, (2022), DOI: 10.1007/s40571-022-00470-0. []
  3. Ruchi Guo, Xu Zhang.
    Solving three-dimensional interface problems with immersed finite elements: a-priori error analysis.
    Journal of Computational Physics, 441 (2021), 110445. []
  4. Derrick Jones, Xu Zhang.
    A conforming-nonconforming mixed immersed finite element method for unsteady Stokes equations with moving interfaces.
    Electronic Research Archive, 29 (2021) no.5 3171-3191. []
  5. Daoru Han, Xiaoming He, David Lund, Xu Zhang.
    PIFE-PIC: Parallel Immersed-Finite-Element Particle-in-Cell for 3-D Kinetic Simulations of Plasma-Material Interactions.
    SIAM Journal on Scientific Computing, 43 (2021), no.3, C235-C257. []
  6. Derrick Jones, Xu Zhang.
    A class of nonconforming immersed finite element methods for Stokes interface problems.
    Journal of Computational and Applied Mathematics, 392 (2021), Article 113493. []
  7. Yuan Chen, Xu Zhang.
    A P2-P1 partially penalized immersed finite element method for Stokes interface problems.
    International Journal of Numerical Analysis & Modeling, 18 (2021), no.1, 120-141. []
  8. Yuan Chen, Songming Hou, Xu Zhang.
    A bilinear partially penalized immersed finite element method for elliptic interface problems with multi-domains and triple junction points.
    Results in Applied Mathematics 8 (2020), Article 100100. []
  9. Cuiyu He, Xu Zhang.
    Residual based a posteriori error estimation for immersed finite element methods.
    Journal of Scientific Computing 81 (2019), no.3, 2051-2079. []
  10. Yuan Chen, Songming Hou, Xu Zhang.
    An immersed finite element method for elliptic interface problems with multi-domain and triple junction points.
    Advances in Applied Mathematics and Mechanics 11 (2019), no.5, 1005-1021. []
  11. Tao Lin, Dongwoo Sheen, Xu Zhang.
    A nonconforming immersed finite element method for elliptic interface problems.
    Journal of Scientific Computing 79 (2019), no.1, 442-463. []
  12. Lin Mu, Xu Zhang.
    An immersed weak Galerkin method for elliptic interface problems.
    Journal of Computational and Applied Mathematics 362 (2019), 471-483. []
  13. Ruchi Guo, Tao Lin, Xu Zhang
    Nonconforming immersed finite element spaces for elliptic interface problems.
    Computers & Mathematics with Applications 75 (2018), no.6, 2002-2016. []
  14. Jinwei Bai, Yong Cao, Yuchuan Chu, Xu Zhang.
    An improved immersed finite element particle-in-cell method for plasma simulation.
    Computers & Mathematics with Applications 75 (2018), no.6, 1887-1899.  []
  15. Ruishu Wang, Ran Zhang, Xu Zhang, Zhimin Zhang.
    Supercloseness analysis and polynomial preserving recovery for a class of weak Galerkin methods.
    Numerical Methods for Partial Differential Equations 34 (2018), no.1, 317-335. []
  16. Waixiang Cao, Xu Zhang, Zhimin Zhang, Qingsong Zou.
    Superconvergence of immersed finite volume methods for one-dimensional interface problems.
    Journal of Scientific Computing 73 (2017), no.2-3, 543-565. [] [Correction]
  17. Waixiang Cao, Xu Zhang, Zhimin Zhang.
    Superconvergence of immersed finite element methods for interface problems.
    Advances in Computational Mathematics 43 (2017), no.4, 795-821. []
  18. Yong Cao, Yuchuan Chu, Xiaoshi Zhang, Xu Zhang.
    Immersed finite element methods for unbounded interface problems with periodic structures.
    Journal of Computational and Applied Mathematics 307 (2016), 72-81. []
  19. Qing Yang, Xu Zhang.
    Discontinuous Galerkin immersed finite element methods for parabolic interface problems.
    Journal of Computational and Applied Mathematics 299 (2016), 127-139. []
  20. Tao Lin, Qing Yang, Xu Zhang.
    Partially penalized immersed finite element methods for parabolic interface problems.
    Numerical Methods for Partial Differential Equations 31 (2015), no.6, 1925-1947. []
  21. Tao Lin, Qing Yang, Xu Zhang.
    A priori error estimates for some discontinuous Galerkin immersed finite element methods.
    Journal of Scientific Computing 65 (2015), no.3, 875-894. []
  22. Tao Lin, Yanping Lin, Xu Zhang.
    Partially penalized immersed finite element methods for elliptic interface problems.
    SIAM Journal on Numerical Analysis 53 (2015), no.2, 1121-1144. []
    (A highly cited paper in Mathematics in Web of Science)
  23. Wenqiang Feng, Xiaoming He, Yanping Lin, Xu Zhang.
    Immersed finite element method for interface problems with algebraic multigrid solver.
    Communications in Computational Physics 15 (2014), no.4, 1045-1067. []
  24. Tao Lin, Dongwoo Sheen, Xu Zhang.
    A locking-free immersed finite element method for planar elasticity interface problems.
    Journal of Computational Physics 247 (2013), 228-247. []
  25. Tao Lin, Yanping Lin, Xu Zhang.
    A method of lines based on immersed finite elements for parabolic moving interface problems.
    Advances in Applied Mathematics and Mechanics 5 (2013), no.4, 548-568. []
  26. Tao Lin, Yanping Lin, Xu Zhang.
    Immersed finite element method of lines for moving interface problems with nonhomogeneous flux jump.
    Contemporary Mathematics 586 (2013), 257-265. []
  27. Xiaoming He, Tao Lin, Yanping Lin, Xu Zhang.
    Immersed finite element methods for parabolic equations with moving interface.
    Numerical Methods for Partial Differential Equations 29 (2013), no.2, 619-646. []
  28. Wenqiang Feng, Xiaoming He, Zhu Wang, Xu Zhang.
    Non-iterative domain decomposition methods for a non-stationary Stokes-Darcy model with Beavers-Joseph interface condition.
    Applied Mathematics and Computation 219 (2012), no.2, 453-463. []
  29. Tao Lin, Xu Zhang.
    Linear and bilinear immersed finite elements for planar elasticity interface problems.
    Journal of Computational and Applied Mathematics 236 (2012), no.18, 4681-4699. []
  30. Guozhu Yu, Xiaoping Xie, Xu Zhang.
    Parameter extension for combined hybrid finite element methods and application to plate bending problems.
    Applied Mathematics and Computation 216 (2010), no.11, 3265-3274. []
  31. Xu Zhang, Guozhu Yu, Xiaoping Xie.
    Fully discrete finite element approximation of a fluid-structure interaction problem.
    Journal of Sichuan University 47 (2010), no.5, 941-947. []

Paper submitted

  1. Cuiyu He, Shun Zhang, Xu Zhang.
    Error Analysis of Petrov Galerkin Immersed Finite Element Methods.
    submitted, (2022).
  2. Yuan Chen, Xu Zhang.
    Solving Navier-Stokes Equations with Stationary and Moving Interfaces on Unfitted Meshes.
    submitted, (2021).

Conference Papers

  1. Derrick Jones, Xu Zhang.
    A high order immersed finite element method for parabolic interface problems.
    ITM Web of Conferences 29 (2019), 01007. []
  2. Chartese Jones, Xu Zhang.
    An efficient numerical method for one-dimensional hyperbolic interface problems.
    ITM Web of Conferences 29 (2019), 01002. []

Ph.D. Dissertation

  1. Nonconforming Immersed Finite Element Methods for Interface Problems
    Virginia Polytechnic Institute and State University (2013). []