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SECOND ORDER UNCONDITIONALLY STABLE AND CONVERGENT LINEARIZED SCheME FOR A FLUID-FLUID INTERACTION MODEL

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Journal of Computational Mathematics 2023年第1期41卷 72-93页

作者： Wei Li Pengzhan Huang yinnian he College of Mathematics and System Sciences Xinjiang UniversityUrumqi 830017China School of Mathematics and Statistics Xi’an Jiaotong UniversityXi’an 710049China

In this paper,a fully discrete finite element scheme with second-order temporal accuracy is proposed for a fluid-fluid interaction model,which consists of two Navier-Stokes equations coupled by a linear interface *** proposed fully discrete scheme is a combination of a mixed finite element approximation for spatial discretization,the secondorder backward differentiation formula for temporal discretization,the second-order Gear’s extrapolation approach for the interface terms and extrapolated treatments in linearization for the nonlinear ***,the unconditional stability is established by rigorous analysis and error estimate for the fully discrete scheme is also ***,some numerical experiments are carried out to verify the theoretical results and illustrate the accuracy and efficiency of the proposed scheme.

关键词： Fluid-fluid interaction model Unconditional stability Second order temporal accuracy Error estimate

A FINITE ELEMENT ALGORITHM FOR NEMATIC LIQUID CRYSTAL FLOW BASED ON The GAUGE-UZAWA METHOD

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Journal of Computational Mathematics 2022年第1期40卷 26-43页

作者： Pengzhan Huang yinnian he Ting Li College of Mathematics and System Sciences Xinjiang UniversityUrumqi 830046China School of Mathematics and Statistics Xi’an Jiaotong UniversityXi’an 710049China

In this paper,we present a finite element algorithm for the time-dependent nematic liquid crystal flow based on the Gauge-Uzawa *** algorithm combines the Gauge and Uzawa methods within a finite element variational formulation,which is a fully discrete projection type algorithm,whereas many projection methods have been studied without space ***,error estimates for velocity and molecular orientation of the nematic liquid crystal flow are ***,numerical results are given to show that the presented algorithm is reliable and confirm the theoretical analysis.

关键词： Nematic liquid crystal model Finite element approximation Gauge-Uzawa method Error analysis

Regularity results of solution uniform in time for complex Ginzburg-Landau equation

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Frontiers of Mathematics in China 2020年第2期15卷 305-315页

作者： yinnian he School of Mathematics and Statistics Xi’an Jiaotong UniversityXi’an 710049China

We provide the H2-regularity result of the solution ip and its first-order time derivative ipt and the second-order time derivative iptt for the complex Ginzburg-Landau equation with the Dirichlet or Neumann boundary *** analysis shows that these regularity results are uniform when t tends to ∞ and 0 and are dependent of the powers of ε^-1.

关键词： Complex Ginzburg-Landau equation(CGL) H^2-regularity sharp a priori estimates

An Uzawa-type algorithm for the coupled Stokes equations

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Applied Mathematics and Mechanics(English Edition) 2020年第7期41卷 1095-1104页

作者： Pengzhan HUANG yinnian he College of Mathematics and System Sciences Xinjiang UniversityUrumqi 830046China School of Mathematics and Statistics Xi’an Jiaotong UniversityXi’an 710049China

An Uzawa-type algorithm is designed for the coupled Stokes equations discretized by the mixed finite element *** velocity solved by the presented algorithm is weakly divergence-free,which is different from the one sol... 详细信息

关键词： coupled Stokes equation Uzawa method optimal relaxation parameter weakly divergence-free

LOCAL AND PARALLEL FINITE ELEMENT ALGORITHMS FOR The NAVIER-STOKES PROBLEM

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Journal of Computational Mathematics 2006年第3期24卷 227-238页

作者： yinnian he Jinchao Xu Aihui Zhou Faculty of Science Xi'an Jiaotong University Xi'an 710049 China Department of Mathematics Penn State University University Park PA 16802 USA LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

Based on two-grid discretizations, in this paper, some new local and parallel finite element algorithms are proposed and analyzed for the stationary incompressible Navier- Stokes problem. These algorithms are motivated by the observation that for a solution to the Navier-Stokes problem, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel procedure. One major technical tool for the analysis is some local a priori error estimates that are also obtained in this paper for the finite element solutions on general shape-regular grids.

关键词： Navier-Stokes problem Finite element Two-grid method Local and parallel algorithm.

Restricted Additive Schwarz Preconditioner for Elliptic Equations with Jump Coefficients

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Advances in Applied Mathematics and Mechanics 2016年第6期8卷 1072-1083页

作者： Zhiyong Liu yinnian he School of Mathematics and Computer Science Ningxia UniversityYinchuan 750021China Center for Computational Geosciences School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’an 710049China

This paper provides a proof of robustness of the restricted additive Schwarz preconditioner with harmonic overlap(RASHO)for the second order elliptic problems with jump *** analyzing the eigenvalue distribution of the RASHO preconditioner,we prove that the convergence rate of preconditioned conjugate gradient method with RASHO preconditioner is uniform with respect to the large jump and meshsize.

关键词： Jump coefficients conjugate gradient effective condition number domain decomposition,restricted additive Schwarz.

Convergence and stability of two-level penalty mixed finite element method for stationary Navier-Stokes equations

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Frontiers of Mathematics in China 2013年第4期8卷 837-854页

作者： Pengzhan HUANG yinnian he Xinlong FENG College of Mathematics and System Sciences Xinjiang University Urumqi 830046 China School of Mathematics and Statistics Xi'an Jiaotong University Xi'an 710049 China

The two-level penalty mixed finite element method for the stationary Navier-Stokes equations based on Taylor-Hood element is considered in this paper. Two algorithms are proposed and analyzed. Moreover, the optimal stability analysis and error estimate for these two algorithms are provided. Finally, the numerical tests confirm the theoretical results of the presented algorithms.

关键词： Navier-Stokes equation level strategy Taylor-Hood element penalty mixed finite element method two-error estimate stability analysis

A SECOND ORDER MODIFIED CHARACTERISTICS VARIATIONAL MULTISCALE FINITE ELEMENT METHOD FOR TIME-DEPENDENT NAVIER-STOKES PROBLEMS

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Journal of Computational Mathematics 2013年第2期31卷 154-174页

作者： Zhiyong Si Jian Su yinnian he School of Mathematics and Information Science Henan Polytechnic University Jiaozuo 454003 China Center for Computational Geosciences School of Mathematics and Statistics Xi 'an Jiaotong University Xi'an 710049 China

In this paper, by combining the second order characteristics time discretization with the variational multiscale finite element method in space we get a second order modified characteristics variational multiscale finite element method for the time dependent Navier- Stokes problem. The theoretical analysis shows that the proposed method has a good convergence property. To show the efficiency of the proposed finite element method, we first present some numerical results for analytical solution problems. We then give some numerical results for the lid-driven cavity flow with Re = 5000, 7500 and 10000. We present the numerical results as the time are sufficient long, so that the steady state numerical solutions can be obtained.

关键词： Modified method of characteristics Defect-correction finite element method Navier-Stokes problems Characteristics-based method Lid-driven problem.

A Stabilized Finite Element Method for Non-Stationary Conduction-Convection Problems

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Advances in Applied Mathematics and Mechanics 2011年第2期3卷 239-258页

作者： Ke Zhao yinnian he Tong Zhang Faculty of Science Xi’an Jiaotong UniversityXi’an 710049ShanxiChina. School of Mathematics&Information Science Henan Polytechnic UniversityJiaozuo 454003HenanChina.

This paper is concerned with a stabilized finite element method based on two local Gauss integrations for the two-dimensional non-stationary conductionconvection equations by using the lowest equal-order pairs of finite *** method only offsets the discrete pressure space by the residual of the simple and symmetry term at element level in order to circumvent the inf-sup *** stability of the discrete scheme is derived under some regularity ***timal error estimates are obtained by applying the standard Galerkin ***,the numerical illustrations agree completely with the theoretical expectations.

关键词： Non-stationary conduction-convection equations finite element method stabilized method stability analysis error estimate