Yinnian He - Academia.edu (original) (raw)

Papers by Yinnian He

In the paper, an inf-sup stabilized finite element method by multiscale functions for the Stokes ... more In the paper, an inf-sup stabilized finite element method by multiscale functions for the Stokes equations is discussed. The key idea is to use a PetrovGalerkin approach based on the enrichment of the standard polynomial space for the velocity component with multiscale functions. The inf-sup condition for P1−P0 triangular element (or Q1−P0 quadrilateral element) is established. The optimal error estimates of the stabilized finite element method for the Stokes equations are obtained. AMS subject classifications: 76D05, 65N30, 35K60

Time-space iterative method Spatial iterative method Stability Error estimate a b s t r a c t Thi... more Time-space iterative method Spatial iterative method Stability Error estimate a b s t r a c t This paper makes some numerical comparisons of time-space iterative method and spatial iterative methods for solving the stationary Navier-Stokes equations. The time-space iterative method consists in solving the nonstationary Stokes equations based on the time-space discretization by the Euler implicit/explicit scheme under a weak uniqueness condition (A2). The spatial iterative methods consist in solving the stationary Stokes scheme, Newton scheme, Oseen scheme based on the spatial discretization under some strong uniqueness assumptions. We compare the stability and convergence conditions of the time-space iterative method and the spatial iterative methods. Moreover, the numerical tests show that the time-space iterative method is the more simple than the spatial iterative methods for solving the stationary Navier-Stokes problem. Furthermore, the time-space iterative method can solve the stationary Navier-Stokes equations with some small viscosity and the spatial iterative methods can only solve the stationary Navier-Stokes equations with some large viscosities.

Based on full domain partition, three parallel iterative finite element algorithms for the statio... more Based on full domain partition, three parallel iterative finite element algorithms for the stationary Navier-Stokes equations are proposed and analyzed. In these algorithms, each subproblem is defined in the entire domain with the vast majority of the degrees of freedom associated with the particular subdomain that it is responsible for and hence can be solved in parallel with other subproblems using an existing sequential solver without extensive recoding. All of the subproblems are nonlinear and are independently solved by three kinds of iterative methods. Under some (strong) uniqueness conditions, errors of the parallel iterative finite element solutions are estimated. Some numerical results are also given which demonstrate the efficiency of the parallel iterative algorithms.

In this paper, it is proved that the probabilities of a real random matrix and a rational random ... more In this paper, it is proved that the probabilities of a real random matrix and a rational random matrix being non-singular are 1 in the matrix computations, respectively. Finally, the applications for the least squares problem are given.

A Galerkin-wavelet scheme is presented for solving the 2-D stationary Navier-Stokes equations usi... more A Galerkin-wavelet scheme is presented for solving the 2-D stationary Navier-Stokes equations using the scaling generator of the divergence free wavelets. Moreover, some ''boundary'' generators are constructed to improve the approximation accuracy. Finally, the optimal error estimates and the numerical results are reported.

In this paper, we considered an important model describing a two-species predator-prey system wit... more In this paper, we considered an important model describing a two-species predator-prey system with diffusion terms and stage structure. By using the linearized method, we investigated the locally asymptotical stability of the nonnegative equilibria of the system and obtained the locally stable conditions. And by using the approach introduced by Canosa [J. Canosa, On a nonlinear diffusion equation describing population growth, IBM J. Res. Dev. 17 (1973) 307-313] and the method of upper and lower solutions, we studied the existence of traveling wavefronts, connecting the zero solution with the positive equilibrium of the system. Our results show that the traveling wavefronts exist and appear to be monotone. Finally, we given a conclusion to summarize the overall achievements of the work presented in the paper.

Nonlinear Analysis: Theory, Methods & Applications, 2008

In this paper, we use the iteration technique for regularity estimates, combining with the classi... more In this paper, we use the iteration technique for regularity estimates, combining with the classical existence theorem of global attractors, to derive that for any k≥0 the semilinear parabolic equation possesses a global attractor in Hk(Ω), which attracts any bounded subset of Hk(Ω) in the Hk-norm.

Numerical Methods for Partial Differential Equations - NUMER METHOD PARTIAL DIFFER E, 2007

Applied Mathematics and Computation, 2007

The new second-order and third-order iterative methods without derivatives are presented for solv... more The new second-order and third-order iterative methods without derivatives are presented for solving nonlinear equations; the iterative formulae based on the homotopy perturbation method are deduced and their convergences are provided. Finally, some numerical experiments show the efficiency of the theoretical results for the above methods.

Mathematical Problems in Engineering - MATH PROBL ENG, 2010

We present a numerical technique based on the coupling of boundary and finite element methods for... more We present a numerical technique based on the coupling of boundary and finite element methods for the steady Oseen equations in an unbounded plane domain. The present paper deals with the implementation of the coupled program in the two-dimensional case. Computational results are given for a particular problem which can be seen as a good test case for the accuracy of the method.

SIAM Journal on Numerical Analysis, 2007

Physics Letters A, 2011

In this Letter, a variable-coefficient discrete (G′G)-expansion method is proposed to seek new an... more In this Letter, a variable-coefficient discrete (G′G)-expansion method is proposed to seek new and more general exact solutions of nonlinear differential–difference equations. Being concise and straightforward, this method is applied to the (2+1)-dimension Toda equation. As a result, many new and more general exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. It is shown

Numerische Mathematik, 2008

Based on two-grid discretizations, in this paper, some new local and parallel finite element algo... more 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.

Numerical Methods for Partial Differential Equations, 2008

$Research paper thumbnail of Analysis of the fractional Kawahara equation using an implicit fully discrete local discontinuous Galerkin method$

Numerical Methods for Partial Differential Equations, 2013

Nonlinear Analysis: Real World Applications, 2009

This paper deals with the convergence and stability of a new parallel algorithm and the error est... more This paper deals with the convergence and stability of a new parallel algorithm and the error estimates for a particular case of the new parallel algorithm, which is used to solve the incompressible nonstationary Navier-Stokes equations. The theoretical results show that the scheme is (at least) conditionally stable and convergent.

Mathematics of Computation, 2007

This paper provides an error analysis for the Crank-Nicolson extrapolation scheme of time discret... more This paper provides an error analysis for the Crank-Nicolson extrapolation scheme of time discretization applied to the spatially discrete stabilized finite element approximation of the two-dimensional time-dependent Navier-Stokes problem, where the finite element space pair (X_h,M_h) for the approximation (u_h^n,p_h^n) of the velocity u and the pressure p is constructed by the low-order finite element: the Q_1-P_0 quadrilateral element or

Mathematical Problems in Engineering, 2011

ABSTRACT

Mathematical Modelling and Analysis, 2012

In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LDG... more In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for a time-fractional Zakharov–Kuznetsov equation. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. We show that our scheme is unconditional stable and L error estimate for the linear case with the convergence rate through analysis.