60 citations · 68 across the 28 of their papers we have counts for
29 papers
Eigenvalue Asymptotics in High-Contrast Media
Huaian Diao, Long Li, Mourad Sini +1
We investigate the eigenfrequency asymptotics of a bounded acoustic cavity containing a shrinking high-contrast inclusion. This configuration is motivated by contrast-enhanced ultr…
Quantum Simulation of Stokes Flow via Schrödingerisation and Artificial Compressibility
Shi Jin, Jiaqi Tang, Qilong Zhai +1
Simulating incompressible Stokes flow is essential for studies in microfluidics and low-Reynolds number hydrodynamics. However, the computational cost of resolving the associated s…
The Immersed Discontinuous Galerkin Method for Elliptic Interface Problems
Lin Yang, Qilong Zhai
This paper is devoted to construction and convergence analysis of the linear explicit immersed finite element (IFE) function. For the interface elements, the proposed IFE functions…
The weak Galerkin method for a class of Gross-Pitaevskii type eigenvalue problems
Wei Lu, Qilong Zhai
This paper aims to employ the weak Galerkin method to solve a class of nonlinear eigenvalue problems. We proved the weak Galerkin scheme produces lower bound for the energy. Moreov…
Regularity Analysis and Tensor Neural Network Methods for Quasiperiodic Elliptic Equations
Jingze Ren, Yifan Wang, Hehu Xie +1
This paper investigates quasiperiodic elliptic equations using a well-established projection method, by which the original problem is reformulated as a degenerate periodic variatio…
Quasiperiodic Elliptic Operators: Projection Method and Convergence Analysis
Kai Jiang, Jiaqi Tang, Qilong Zhai +1
Quasiperiodic elliptic operators (QEOs) serve as fundamental models in both mathematics and physics, as exemplified by their role in the numerical modeling of one-dimensional photo…
A posteriori error estimation for weak Galerkin method of the fourth-order singularly perturbed problem
Shicheng Liu, Qilong Zhai
In this paper, we present a posteriori error estimation for weak Galerkin method applied to fourth order singularly perturbed problem. The weak Galerkin discretization space and nu…
The two-grid weak Galerkin method and enriched Crouzeix-Raviart element method for linear elastic eigenvalue problems
Wei Lu, Qilong Zhai
In this paper, we present a two-gird skill to accelerate the weak Galerkin method. By the proper use of parameters, the two-grid weak Galerkin method not only doubles the convergen…
The Weak Galerkin and Crouzeix-Raviart element method for elastic eigenvalue problems
Wei Lu, Hehu Xie, Qilong Zhai
In this paper, we first introduce an abstract framework to solve the eigenvalue problem by weak Galerkin (WG) method. By the application of the framework, WG method is proved to be…
The Immersed Skeletal Finite Element Method for Elliptic Interface Problems
Lin Yang, Qilong Zhai
In this paper, we present a new immersed finite element scheme for solving elliptic interface problems on unfitted meshes by combining the skeletal finite element method (FEM) with…
The pressure-robust weak Galerkin finite element method for Stokes-Darcy problem
Jiwei Jia, Lin Yang, Qilong Zhai
In this paper, we propose a pressure-robust weak Galerkin (WG) finite element scheme to solve the Stokes-Darcy problem. To construct the pressure-robust numerical scheme, we use th…
Convergence analysis of a weak Galerkin finite element method on a Bakhvalov-type mesh for a singularly perturbed convection-diffusion equation in 2D
Shicheng Liu, Xiangyun Meng, Qilong Zhai
In this paper, we propose a weak Galerkin finite element method (WG) for solving singularly perturbed convection-diffusion problems on a Bakhvalov-type mesh in 2D. Our method is fl…
A weak Galerkin finite element method for solving the asymptotic lower bound of Maxwell eigenvalue problem
Shusheng Li, Qilong Zhai
In this paper, we propose a weak Galerkin (WG) finite element method for the Maxwell eigenvalue problem. By restricting subspaces, we transform the mixed form of Maxwell eigenvalue…
A stabilizer free weak Galerkin method with implicit -schemes for fourth order parabolic problems
Shanshan Gu, Qilong Zhai
In this paper, we combine the stabilizer free weak Galerkin (SFWG) method and the implicit -schemes in time for to solve the fourth-order parabolic proble…
The stabilizer-free weak Galerkin finite element method for the Biharmonic equation using polynomials of reduced order
Shanshan Gu, Qilong Zhai
In this article, we decrease the degree of the polynomials on the boundary of the weak functions and modify the definition of the weak laplacian which are introduced in \cite{Bihar…
Weak Galerkin methods for the Stokes eigenvalue problem
Yunying Fan, Qilong Zhai
In this paper, we rewrite the Stokes eigenvalue problem as an Elliptic eigenvalue problem restricted to subspace, and introduce an abstract framework of solving abstract elliptic e…
Convergence analysis of a weak Galerkin finite element method on a Shishkin mesh for a singularly perturbed fourth-order problem in 2D
Shicheng Liu, Xiangyun Meng, Qilong Zhai
We consider the singularly perturbed fourth-order boundary value problem on the unit square , with boundary conditions $u = \p…
The weak Galerkin finite element method for the Steklov eigenvalue problem
Shusheng Li, Hehu Xie, Qilong Zhai
This paper introduces the application of the weak Galerkin (WG) finite element method to solve the Steklov eigenvalue problem, focusing on obtaining lower bounds of the eigenvalues…
A locking-free mixed enriched Galerkin method of arbitrary order for linear elasticity using the stress-displacement formulation
Zhongshu Zhao, Hui Peng, Qilong Zhai +1
In this paper, we develop an arbitrary-order locking-free enriched Galerkin method for the linear elasticity problem using the stress-displacement formulation in both two and three…
A conforming discontinuous Galerkin finite element method for Brinkman equations
Haoning Dang, Qilong Zhai, Zhongshu Zhao
In this paper, we present a conforming discontinuous Galerkin (CDG) finite element method for Brinkman equations. The velocity stabilizer is removed by employing the higher degree…
The weak Galerkin finite element method for Stokes interface problems with curved interface
Lin Yang, Qilong Zhai, Ran Zhang
In this paper, we develop a new weak Galerkin finite element scheme for the Stokes interface problem with curved interfaces. We take a unique vector-valued function at the interfac…
A weak Galerkin-mixed finite element method for the Stokes-Darcy problem
Hui Peng, Qilong Zhai, Ran Zhang +1
In this paper, we propose a new numerical scheme for the coupled Stokes-Darcy model with Beavers-Joseph-Saffman interface condition. We use the weak Galerkin method to discretize t…
The Shifted-inverse Power Weak Galerkin Method for Eigenvalue Problems
Qilong Zhai, Xiaozhe Hu, Ran Zhang
This paper proposes and analyzes a new weak Galerkin method for the eigenvalue problem by using the shifted-inverse power technique. A high order lower bound can be obtained at a r…
Acceleration of weak Galerkin methods for the Laplacian eigenvalue problem
Qilong Zhai, Hehu Xie, Ran Zhang +1
Recently, we proposed a weak Galerkin finite element method for the Laplace eigenvalue problem. In this paper, we present two-grid and two-space skills to accelerate the weak Galer…