259 citations · 554 across the 15 of their papers we have counts for
16 papers
A Structural Relationship Between Crouzeix-Raviart Immersed Finite Elements for Elliptic and Stokes Interface Problems
Jiaying Ren, Guozhu Yu, Xu Zhang
In this paper, we study the structural relationship between immersed finite element (IFE) spaces for scalar elliptic and Stokes interface problems on unfitted meshes. Although IFE…
A Priori Error Analysis of a High-Order Selective Discontinuous Galerkin Method for Elliptic Interface Problems
Fang Liu, Haroun Meghaichi, Xu Zhang
This paper develops a high-order selective discontinuous Galerkin (SDG) method for solving elliptic interface problems on interface-unfitted Cartesian meshes. This method applies t…
PIFE-PIC: Parallel Immersed-Finite-Element Particle-In-Cell For 3-D Kinetic Simulations of Plasma-Material Interactions
Daoru Han, Xiaoming He, David Lund +1
This paper presents a recently developed particle simulation code package PIFE-PIC, which is a novel three-dimensional (3-D) Parallel Immersed-Finite-Element (IFE) Particle-in-Cell…
Solving Three-Dimensional Interface Problems with Immersed Finite Elements: A-Priori Error Analysis
Ruchi Guo, Xu Zhang
In this paper, we develop and analyze a trilinear immersed finite element method for solving three-dimensional elliptic interface problems. The proposed method can be utilized on i…
A Bilinear Partially Penalized Immersed Finite Element Method for Elliptic Interface Problems with Multi-Domains and Triple-Junction Points
Yuan Chen, Songming Hou, Xu Zhang
In this article, we introduce a new partially penalized immersed finite element method (IFEM) for solving elliptic interface problems with multi-domains and triple-junction points.…
Residual-based a posteriori error estimation for immersed finite element methods
Cuiyu He, Xu Zhang
In this paper we introduce and analyze the residual-based a posteriori error estimation of the partially penalized immersed finite element method for solving elliptic interface pro…
An Immersed Weak Galerkin Method For Elliptic Interface Problems
Lin Mu, Xu Zhang
In this paper, we present an immersed weak Galerkin method for solving second-order elliptic interface problems. The proposed method does not require the meshes to be aligned with…
An improved immersed finte element particle-in-cell method for plasma simulation
Jinwei Bai, Yong Cao, Yuchuan Chu +1
The particle-in-cell (PIC) method has been widely used for plasma simulation, because of its noise-reduction capability and moderate computational cost. The immersed finite element…
Superconvergence of immersed finite volume methods for one-dimensional interface problems
Waixiang Cao, Xu Zhang, Zhimin Zhang +1
In this paper, we introduce a class of high order immersed finite volume methods (IFVM) for one-dimensional interface problems. We show the optimal convergence of IFVM in H1 and L2…
Nonconforming Immersed Finite Element Spaces For Elliptic Interface Problems
Ruchi Guo, Tao Lin, Xu Zhang
In this paper, we use a unified framework introduced in [3] to study two classes of nonconforming immersed finite element (IFE) spaces with integral value degrees of freedom. The s…
Supercloseness analysis and polynomial preserving recovery for a class of weak Galerkin method
Ruishu Wang, Ran Zhang, Xu Zhang +1
In this paper, we analyze convergence and supercloseness properties of a class of weak Galerkin (WG) finite element methods for solving second-order elliptic problems. It is shown…
Superconvergence of Immersed Finite Element Methods for Interface Problems
Waixiang Cao, Xu Zhang, Zhimin Zhang
In this article, we study superconvergence properties of immersed finite element methods for the one dimensional elliptic interface problem. Due to low global regularity of the sol…
A nonconforming immersed finite element method for elliptic interface problems
Tao Lin, Dongwoo Sheen, Xu Zhang
A new immersed finite element (IFE) method is developed for second-order elliptic problems with discontinuous diffusion coefficient. The IFE space is constructed based on the rotat…
Discontinuous Galerkin Immersed Finite Element Methods for Parabolic Interface Problems
Qing Yang, Xu Zhang
In this article, interior penalty discontinuous Galerkin methods using immersed finite element functions are employed to solve parabolic interface problems. Typical semi-discrete a…
A Priori Error Estimates for Some Discontinuous Galerkin Immersed Finite Element Methods
Tao Lin, Qing Yang, Xu Zhang
In this paper, we derive a priori error estimates for a class of interior penalty discontinuous Galerkin (DG) methods using immersed finite element (IFE) functions for a classic se…
Partially Penalized Immersed Finite Element Methods for Elliptic Interface Problems
Tao Lin, Yanping Lin, Xu Zhang
This article presents new immersed finite element (IFE) methods for solving the popular second order elliptic interface problems on structured Cartesian meshes even if the involved…