Xu Zhang's Homepage

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1. Qiao Zhuang, Xu Zhang.
   A Unified Interface Neural Network for Elliptic Interface Problems.
   Submitted. (2026), arXiv:2610.25409. [ ]
2. Yuanhui Lin, Xu Zhang, Tao Lin, Minfu Feng.
   Geometry‐Conforming Finite Element Methods for Interface Problems on Fitted and Unfitted Meshes.
   Submitted. (2026), arXiv:2608.14484. [ ]
3. Fang Liu, Haroun Meghaichi, Xu Zhang.
   A Priori Error Analysis of a High-Order Selective Discontinuous Galerkin Method for Elliptic Interface Problems.
   Submitted. (2026), arXiv:2605.19039. [ ]
4. Cuiyu He, Nam Tran, Xu Zhang.
   A Posteriori Error Estimates for Immersed Discontinuous Galerkin Method with Hanging Nodes.
   Journal of Scientific Computing, under revision. (2026). [ ]
5. Ruchi Guo, Xu Zhang.
   An Enriched Immersed Finite Element Method for 3D Interface Problems.
   Science China Mathematics, under revision, (2026) , arXiv:2505.03598. [ ]
6. Jiaying Ren, Guozhu Yu, Xu Zhang.
   A Structural Relationship Between Crouzeix Raviart Immersed Finite Elements for Elliptic and Stokes Interface Problems.
   Numerical Methods for Partial Differential Equations, 42, (2026), no. 5, e70143 [ ]
7. Yuanhui Lin, Xu Zhang, Tao Lin.
   Frenet Immersed Finite Element Spaces on Triangular Meshes.
   International Journal of Numerical Analysis and Modeling, in press, (2026). DOI: 10.4208/ijnam2027-1005 [ ]
8. Yuan Chen, Xu Zhang.
   An Immersed C0 Interior Penalty Method for Biharmonic Interface Problems.
   Journal of Scientific Computing, 108, (2026), 38. [ ]
9. Yuan Chen, Xu Zhang.
   Solving Navier-Stokes Equations with Stationary and Moving Interfaces on Unfitted Meshes.
   Journal of Scientific Computing, 98, (2024), 19. [ ]
10. Yuan Chen, Songming Hou, Xu Zhang.
    Semi and fully discrete error analysis for elastodynamic interface problems using immersed finite element methods.
    Computers & Mathematics with Applications, 147, (2023), 92–110. [ ]
11. Cuiyu He, Shun Zhang, Xu Zhang.
    Error Analysis of Petrov-Galerkin Immersed Finite Element Methods.
    Computer Methods in Applied Mechanics and Engineering, 404 (2023), 115744. [ ]
12. Jing Wang, Xu Zhang, Qiao Zhuang.
    An Immersed Crouzeix-Raviart Finite Element Method for Navier-Stokes Interface Problems.
    International Journal of Numerical Analysis and Modeling, 19 (2022), no. 4, 563-586. [ ]
13. 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, 9 (2022), 1279–1291. [ ]
    
14. Ruchi Guo, Xu Zhang.
    Solving three-dimensional interface problems with immersed finite elements: a priori error analysis.
    Journal of Computational Physics, 441 (2021), 110445. [ ]
    
15. 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. [ ]
    
16. 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. [ ]
    
17. 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. [ ]
    
18. Yuan Chen, Xu Zhang.
    A P2-P1 partially penalized immersed finite element method for Stokes interface problems.
    International Journal of Numerical Analysis and Modeling, 18 (2021), no. 1, 120–141. [ ]
19. 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. [ ]
20. 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. [ ]
21. 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. [ ]
22. 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. [ ]
23. Lin Mu, Xu Zhang.
    An immersed weak Galerkin method for elliptic interface problems.
    Journal of Computational and Applied Mathematics 362 (2019), 471–483. [ ]
24. 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. [ ]
25. 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. [ ]
26. 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. [ ]
27. 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 ]
28. 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. [ ]
29. 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. [ ]
30. Qing Yang, Xu Zhang.
    Discontinuous Galerkin immersed finite element methods for parabolic interface problems.
    Journal of Computational and Applied Mathematics 299 (2016), 127–139. [ ]
31. 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. [ ]
32. 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. [ ]
33. 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 )
34. 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. [ ]
35. 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. [ ]
36. 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. [ ]
37. 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. [ ]
38. 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. [ ]
39. 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. [ ]
40. 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. [ ]
41. 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. [ ]
42. 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. [ ]

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). [ ]