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| 1 | A hybridized weak Galerkin finite element scheme for the Stokes equations显示文摘In this paper a hybridized weak Galerkin(HWG) finite element method for solving the Stokes equations in the primary velocity-pressure formulation is introduced.The WG method uses weak functions and their weak derivatives which are defined as distributions.Weak functions and weak derivatives can be approximated by piecewise polynomials with various degrees.Different combination of polynomial spaces leads to different WG finite element methods,which makes WG methods highly flexible and efficient in practical computation.A Lagrange multiplier is introduced to provide a numerical approximation for certain derivatives of the exact solution.With this new feature,the HWG method can be used to deal with jumps of the functions and their flux easily.Optimal order error estimates are established for the corresponding HWG finite element approximations for both primal variables and the Lagrange multiplier.A Schur complement formulation of the HWG method is derived for implementation purpose.The validity of the theoretical results is demonstrated in numerical tests. | ZHAI QiLong ZHANG Ran WANG XiaoShen | 2015 | Science China Mathematics2015，58，11： | 10 |
| 2 | Zacopride selectively activates the Kir2.1 channel via a PKA signaling pathway in rat cardiomyocytes显示文摘We recently reported that zacopride is a selective inward rectifier potassium current (IK1 ) channel agonist, suppressing ventricular arrhythmias without affecting atrial arrhythmias. The present study aimed to investigate the unique pharmacological properties of zacopride. The whole-cell patch-clamp technique was used to study IK1 currents in rat atrial myocytes and Kir2.x currents in human embryonic kidney (HEK)-293 cells transfected with inward rectifier potassium channel (Kir)2.1, Kir2.2, Kir2.3, or mutated Kir2.1 (at phosphorylation site S425L). Western immunoblots were performed to estimate the relative protein expression levels of Kir2.x in rat atria and ventricles. Results showed that zacopride did not affect the IK1 and transmembrane potential of atrial myocytes. In HEK293 cells, zacopride increased Kir2.1 homomeric channels by 40.7%±9.7% at 50 mV, but did not affect Kir2.2 and Kir2.3 homomeric channels, and Kir2.1-Kir2.2, Kir2.1-Kir2.3 and Kir2.2-Kir2.3 heteromeric channels. Western immunoblots showed that similar levels of Kir2.3 protein were expressed in rat atria and ventricles, but atrial Kir2.1 protein level was only 25% of that measured in the ventricle. In addition, 5-hydroxytryptamine (5-HT) 3 receptor was undetectable, whereas 5-HT 4 receptor was weakly expressed in HEK293 cells. The Kir2.1-activating effect of zacopride in these cells was abolished by inhibition of protein kinase A (PKA), but not PKC or PKG. Furthermore, zacopride did not activate the mutant Kir2.1 channel in HEK293 cells but selectively activated the Kir2.1 homomeric channel via a PKA-dependent pathway, independent to that of the 5-HT receptor. | ZHANG Li LIU QingHua LIU ChengFang ZHAI XuWen FENG QiLong XU RuiLing CUI XiangLi ZHAO ZhiQing CAO JiMin WU BoWei | 2013 | Science China(Life Sciences)2013，56，9： | 7 |
| 3 | The Weak Galerkin Method for Elliptic Eigenvalue Problems显示文摘This article is devoted to studying the application of the weak Galerkin(WG)finite element method to the elliptic eigenvalue problem with an emphasis on obtaining lower bounds.The WG method uses discontinuous polynomials on polygonal or polyhedral finite element partitions.The non-conforming finite element space of the WG method is the key of the lower bound property.It also makes the WG method more robust and flexible in solving eigenvalue problems.We demonstrate that the WG method can achieve arbitrary high convergence order.This is in contrast with existing nonconforming finite element methods which can provide lower bound approximations by linear finite elements.Numerical results are presented to demonstrate the efficiency and accuracy of the theoretical results. | Qilong Zhai Hehu Xie Ran Zhang Zhimin Zhang | 2019 | Communications in Computational Physics2019，26，6： | 1 |
| 4 | Weak Galerkin Method for Second-Order Elliptic Equations with Newton Boundary Condition显示文摘The weak Galerkin(WG)method is a nonconforming numerical method for solving partial differential equations.In this paper,we introduce the WG method for elliptic equations with Newton boundary condition in bounded domains.The Newton boundary condition is a nonlinear boundary condition arising from science and engineering applications.We prove the well-posedness of the WG scheme by the monotone operator theory and the embedding inequality of weak finite element functions.The error estimates are derived.Numerical experiments are presented to verify the theoretical analysis. | Mingze Qin Ruishu Wang Qilong Zhai Ran Zhang | 2023 | Communications in Computational Physics2023，33，2： | 0 |
| 5 | The Weak Galerkin Method for Linear Hyperbolic Equation显示文摘The linear hyperbolic equation is of great interest inmany branches of physics and industry.In this paper,we use theweak Galerkinmethod to solve the linear hyperbolic equation.Since the weak Galerkin finite element space consists of discontinuous polynomials,the discontinuous feature of the equation can be maintained.The optimal error estimates are proved.Some numerical experiments are provided to verify the efficiency of the method. | Qilong Zhai Ran Zhang Nolisa Malluwawadu Saqib Hussain | 2018 | Communications in Computational Physics2018，24，6： | 0 |
| 6 | Storage and Parallel Loading System Based on Mode Network for Multimode Medical Image Data显示文摘Since Multimode data is composed of many modes and their complex relationships,it cannot be retrieved or mined effectively by utilizing traditional analysis and processing techniques for single mode data.To address the challenges,we design and implement a graph-based storage and parallel loading system aimed at multimode medical image data.The system is a framework designed to flexibly store and rapidly load these multimode data.Specifically,the system utilizes the Mode Network to model the modes and their relationships in multimode medical image data and the graph database to store the data with a parallel loading technique. | Xiao Zhai Haiwei Pan Xiaoqin Xie Zhiqiang Zhang Qilong Han | 2016 | 国际计算机前沿大会会议论文集2016，，2： | 0 |
| 7 | THE SHIFTED-INVERSE POWER WEAK GALERKIN METHOD FOR EIGENVALUE PROBLEMS显示文摘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 relatively low cost via the proposed method.The error estimates for both eigenvalue and eigenfunction are provided and asymptotic lower bounds are shown as well under some conditions.Numerical examples are presented to validate the theoretical analysis. | Qilong Zhai Xiaozhe Hu Ran Zhang | 2020 | Journal of Computational Mathematics2020，38，4： | 0 |
| 8 | A weak Galerkin-mixed finite element method for the Stokes-Darcy problem显示文摘In this paper,we propose a new numerical scheme for the coupled Stokes-Darcy model with the Beavers-Joseph-Saffman interface condition.We use the weak Galerkin method to discretize the Stokes equation and the mixed finite element method to discretize the Darcy equation.A discrete inf-sup condition is proved and the optimal error estimates are also derived.Numerical experiments validate the theoretical analysis. | Hui Peng Qilong Zhai Ran Zhang Shangyou Zhang | 2021 | Science China Mathematics2021，64，10： | 0 |
| 9 | TheWeak Galerkin Finite Element Method for Solving the Time-Dependent Integro-Differential Equations显示文摘In this paper,we solve linear parabolic integral differential equations using the weak Galerkin finite element method(WG)by adding a stabilizer.The semidiscrete and fully-discrete weak Galerkin finite element schemes are constructed.Optimal convergent orders of the solution of the WG in L^(2) and H^(1) norm are derived.Several computational results confirm the correctness and efficiency of the method. | Xiuli Wang Qilong Zhai Ran Zhang Shangyou Zhang | 2020 | Advances in Applied Mathematics and Mechanics2020，12，1： | 0 |
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