Yanping Chen

South China Normal University

113Publications

24H-index

1,857Citations

Publications 113

Newest

Numerical solution of two-dimensional nonlinear Schrödinger equation using a new two-grid finite element method

#1Hanzhang Hu (Jiaying University)

#2Yanping Chen (SCNU: South China Normal University)H-Index: 24

Abstract A new two-grid finite element scheme is presented for two-dimensional nonlinear Schrodinger equation. One Newton iteration is applied on the fine grid to linearize the nonlinear system using the coarse-grid solution as the initial guess, and furthermore one more linear system on the coarse space is solved. The error estimations of the two-grid solution in the L 2 and H 1 norm are given. It is shown, both theoretically and numerically, that the coarse space can be extremely coarse and tw...

Two grid finite element discretization method for semi‐linear hyperbolic integro‐differential equations

#1Luoping Chen (Southwest Jiaotong University)

#2Yanping Chen (SCNU: South China Normal University)H-Index: 24

Last.Yunqing Huang (XTU: Xiangtan University)H-Index: 22

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#1Yanping Chen (SCNU: South China Normal University)H-Index: 24

#2Xin Zhao (XTU: Xiangtan University)

Last.Yunqing Huang (XTU: Xiangtan University)H-Index: 22

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In this paper, we investigate a mortar element method for the time dependent coupling of incompressible flow and porous media flow which are governed by non-stationary Stokes and Darcy equations, respectively. The interface conditions are given by mass conservation, the balance of the normal forces and the Beavers–Joseph–Saffman law. We consider the dual-mixed formulation in Darcy region where velocity and pressure are both unknowns. We employ the lowest order Raviart–Thomas element for Darcy fl...

A Jacobi Spectral Method for Solving Multidimensional Linear Volterra Integral Equation of the Second Kind

#1Yunxia Wei (ZJU: Zhejiang University)H-Index: 1

#2Yanping Chen (SCNU: South China Normal University)H-Index: 24

The subject of the present paper is to apply the Jacobi spectral collocation method for multidimensional linear Volterra integral equation with a weakly singular kernel. Here, we assume that the solution is sufficiently smooth. An error analysis has been provided which justifies that the approximate solution converges exponentially to the exact solution. Finally, two numerical examples are given to clarify the efficiency and accuracy of the method.

Two-grid method for the two-dimensional time-dependent Schrödinger equation by the finite element method

#1Zhikun Tian (XTU: Xiangtan University)H-Index: 1

#2Yanping Chen (SCNU: South China Normal University)H-Index: 24

Last.Jianyun Wang (Hunan University of Technology)

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Abstract In this paper, we construct a backward Euler full-discrete two-grid finite element scheme for the two-dimensional time-dependent Schrodinger equation. With this method, the solution of the original problem on the fine grid is reduced to the solution of same problem on a much coarser grid together with the solution of two Poisson equations on the same fine grid. We analyze the error estimate of the standard finite element solution and the two-grid solution in the H 1 norm. It is shown th...

A priori error estimates of a meshless method for optimal control problems of stochastic elliptic PDEs

#1Fenglin Huang (Xinyang Normal University)

#2Yanping Chen (SCNU: South China Normal University)H-Index: 24

Last.Yunqing Huang (Xinyang Normal University)

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ABSTRACTIn this paper, we study the optimal control problems of stochastic elliptic equations with random field in its coefficients. The main contributions of this work are two aspects. Firstly, a meshless method coupled with the stochastic Galerkin method is investigated to approximate the control problems, which is competitive for high-dimensional random inputs. Secondly, a priori error estimates are derived for the solutions to the control problems. Some numerical tests are carried out to con...

A Legendre–Petrov–Galerkin method for solving Volterra integro-differential equations with proportional delays

#1Haotao Cai (XTU: Xiangtan University)

#2Yanping Chen (SCNU: South China Normal University)H-Index: 24

Last.Yunqing Huang (XTU: Xiangtan University)H-Index: 22

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ABSTRACTIn this paper, a fully discrete Legendre–Petrov–Galerkin method is presented for solving functional Volterra integro-differential equations with vanishing delays. This method produces a fully discrete linear system. We prove that this system has a unique solution for sufficiently large n, where n+1 denotes the order of the system. Moreover, we prove that the approximate solution and its corresponding derivative function arrive at an optimal convergence order O(n−m−1) and O(n−m) in L2 nor...

#1Yunxia Wei (ZJU: Zhejiang University)H-Index: 1

#2Yanping Chen (SCNU: South China Normal University)H-Index: 24

Last.Yuanyuan Zhang (Yantai University)

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This paper is concerned with obtaining an approximate solution for a linear multidimensional Volterra integral equation with a regular kernel. We choose the Gauss points associated with the multidimensional Jacobi weight function \(\omega(x) = \prod{_{i=1}^d}(1 - x_i)^\alpha(1 + x_i)^\beta, -1 <\alpha,\beta < \frac{1}{d} - \frac{1}{2}\) (d denotes the space dimensions) as the collocation points. We demonstrate that the errors of approximate solution decay exponentially. Numerical results are pre...

#1Chuanjun Chen (Yantai University)H-Index: 1

#2Kang Li (Yantai University)H-Index: 1

Last.Yunqing Huang (XTU: Xiangtan University)H-Index: 22

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In this paper, we present a second-order accurate Crank-Nicolson scheme for the two-grid finite element methods of the nonlinear Sobolev equations. This method involves solving a small nonlinear system on a coarse mesh with mesh size H and a linear system on a fine mesh with mesh size h, which can still maintain the asymptotically optimal accuracy compared with the standard finite element method. However, the two-grid scheme can reduce workload and save a lot of CPU time. The optimal error estim...

#2Yanping Chen (SCNU: South China Normal University)H-Index: 24

In this article, we study the Volterra integral equations with two kinds of delay that are proportional delay and nonproportional delay. We mainly use Chebyshev spectral collocation method to analyze them. First, we use variable transformation to transform the equation into an new equation which is defined in [−1, 1]. Then, with the help of Gronwall inequality and some other lemmas, we provide a rigorous error analysis for the proposed method, which shows that the numerical error decay exponenti...

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