Journal Publications
- Yuan Chen, Xu Zhang.
Solving Navier-Stokes Equations with Stationary and Moving Interfaces on Unfitted Meshes.
Journal of Scientific Computing, 98, (2024), 19.
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- 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.
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- 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. []
- 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. []
- 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. []
- Ruchi Guo, Xu Zhang.
Solving three-dimensional interface problems with immersed finite elements: a-priori error analysis.
Journal of Computational Physics, 441 (2021), 110445. []
- 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.
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- 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.
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- 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.
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- 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.
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- 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.
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- 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.
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- 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.
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- 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.
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- Lin Mu, Xu Zhang.
An immersed weak Galerkin method for elliptic interface problems.
Journal of Computational and Applied Mathematics 362 (2019), 471-483.
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- 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.
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- 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.
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- 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.
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- 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.
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[Correction]
- 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.
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- 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.
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- Qing Yang, Xu Zhang.
Discontinuous Galerkin immersed finite element methods for parabolic interface problems.
Journal of Computational and Applied Mathematics 299 (2016), 127-139.
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- 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.
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- 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.
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- 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.
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(A highly cited paper in Mathematics in Web of Science)
- 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.
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- 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.
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- 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.
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- 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.
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- 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.
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- 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.
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- 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.
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- 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.
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- 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.
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Conference Papers
- Derrick Jones, Xu Zhang.
A high order immersed finite element method for parabolic interface problems.
ITM Web of Conferences 29 (2019), 01007.
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- Chartese Jones, Xu Zhang.
An efficient numerical method for one-dimensional hyperbolic interface problems.
ITM Web of Conferences 29 (2019), 01002.
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Ph.D. Dissertation
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Nonconforming Immersed Finite Element Methods for Interface Problems
Virginia Polytechnic Institute and State University (2013).
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