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Superconvergence and asymptotic expansions for bilinear finite volume element approximation on non-uniform grids

Journal of computational and Applied Mathematics 2017年 321卷 323-335页

作者： Cunyun Nie Shi Shu Haiyuan Yu Wenhua Xia The School of Science Hunan Institute of Engineering 411104 China Hunan Key Laboratory for Computation & Simulation in Science and Engineering Xiangtan University Hunan 411105 China Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education Xiangtan University Hunan 411105 China

We initially derive an asymptotic expansion and a high accuracy combination formula of the derivatives in the sense of pointwise for the isoparametric bilinear finite volume element scheme by employing the energy-embedded method on some non-uniform grids. Furthermore, we prove that the approximate derivatives are convergent of order two. Numerical examples confirm theoretical results.

关键词： Isoparametric bilinear finite volume element scheme Non-uniform grids Asymptotic expansion Superconvergence

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Stochastic fractional integro-differential equations with weakly singular kernels: Well-posedness and Euler–Maruyama approximation

arXiv

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arXiv 2019年

作者： Dai, Xinjie Xiao, Aiguo Bu, Weiping School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan411105 China

This paper considers the initial value problem of general nonlinear stochastic fractional integro-differential equations with weakly singular kernels. Our effort is devoted to establishing some fine estimates to include all the cases of Abel-type singular kernels. Firstly, the existence, uniqueness and continuous dependence on the initial value of the true solution under local Lipschitz condition and linear growth condition are derived in detail. Secondly, the Euler–Maruyama method is developed for solving numerically the equation, and then its strong convergence is proven under the same conditions as the well-posedness. Moreover, we obtain the accurate convergence rate of this method under global Lipschitz condition and linear growth condition. In particular, the Euler–Maruyama method can reach strong first-order superconvergence when α = 1. Finally, several numerical tests are reported for verification of the theoretical *** Codes 65C30, 65C20, 65L05, 65L20 Copyright © 201., The Authors. All rights reserved.

关键词： Stochastic systems

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Space-time finite element method for the distributed-order time fractional reaction diffusion equations

Space-time finite element method for the distributed-order t...

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第十六届全国微分方程数值方法暨第十三届全国仿真算法学术会议

作者： Weiping Bu School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityHunan 411105China

In this paper,we propose a space-time finite element method for the distributed-order time fractional reaction diffusion equations(DOTFRDEs).

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A Novel Finite Volume Scheme with Geometric Average Method for Radiative Heat Transfer Problems

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应用物理前沿（中英文版） 2013年第4期1卷 32-44页

作者： Cunyun Nie Haiyuan Yu Department of Mathematics and Physics Hunan Institution of Engineering Xiangtan Hunan 411104 China Hunan Key Laboratory for Computation & Simulation in Science and Engineering and Key Laboratory ofIntelligent Computing & Information Processing of Ministry of Education Xiangtan University Hunan 411105China

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Local convergence analysis of L1.finite element scheme for a constant delay reaction-subdiffusion equation with uniform time mesh

arXiv

引用

arXiv 2024年

作者： Bu, Weiping Zheng, Xin School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan411105 China

The aim of this paper is to develop a refined error estimate of L1.finite element scheme for a reaction-subdiffusion equation with constant delay τ and uniform time mesh. Under the non-uniform multi-singularity assumption of exact solution in time, the local truncation errors of the L1.scheme with uniform mesh is investigated. Then we introduce a fully discrete finite element scheme of the considered problem. Next, a novel discrete fractional Grönwall inequality with constant delay term is proposed, which does not include the increasing Mittag-Leffler function comparing with some popular other cases. By applying this Grönwall inequality, we obtain the pointwisein-time and piecewise-in-time error estimates of the finite element scheme without the Mittag-Leffler function. In particular, the latter shows that, for the considered interval ((i-1.τ, iτ], although the convergence in time is low for i = 1. it will be improved as the increasing i, which is consistent with the factual assumption that the smoothness of the solution will be improved as the increasing i. Finally, we present some numerical tests to verify the developed theory. Copyright © 2024, The Authors. All rights reserved.

关键词： Finite element method

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New upper and lower eigenvalue bounds for the solution of the continuous algebraic riccati equation

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Asian Journal of Control 2014年第1期16卷 284-291页

作者： Liu, Jianzhou Zhang, Juan Department of Mathematics and Computational Science Xiangtan University Xiangtan Hunan 411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan 411105 China

In this paper, applying majorization inequalities, new upper and lower bounds for summation of eigenvalues (including the trace) of the solution of the continuous algebraic Riccati equation are presented. Corresponding numerical examples illustrate that our new bounds extend some of the recent results. © 201. John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society.

关键词： Eigenvalues and eigenfunctions

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Evolution of the electronic and magnetic properties of zigzag silicene nanoribbon used for hydrogen storage material

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International Journal of Hydrogen Energy 2017年第44期42卷 27184-27205页

作者： Yuliang Mao Chan Tang Gang Guo Jianmei Yuan Jianxin Zhong Hunan Key Laboratory for Micro–Nano Energy Materials and Devices School of Physics and Optoelectronic Engineering Xiangtan University Hunan 411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan 411105 China

Using first-principles calculations, we investigate the evolution of electronic and magnetic properties of zigzag silicene nanoribbon (ZSiNR) along with the concentration of edge adsorbed hydrogen adatoms. Our study shows that the significant covalent bonding helps to stabilize the configurations of hydrogen adsorbed ZSiNRs. The ferro-metallic electronic property of ZSiNR originated from the σ-π mixing effect is suppressed by mono-hydrogenation at the adsorption sites due to the sp 2 bonding. However, bi-hydrogenation at the adsorbed sites will lead to the typical sp 3 bonding, which dominates the electronic property with the increasing of hydrogen adatoms. Under the coexisting situation with mono-hydrogenation and bi-hydrogenation, we find that both the number of adsorption sites and the bonding type of sp 2 or sp 3 have impact on the electronic property of ZSiNR. It is found that symmetry adsorption at the edges changes the stable magnetic state of ZSiNR from ferromagnetic to antiferromagnetic. In contrast, unsymmetrical adsorption along the two edges of ZSiNR keeps its ferromagnetic property.

关键词： Silicene nanoribbon Hydrogen adatom First-principles Edge-adsorption

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The Mean Time to Absorption on Horizontal Partitioned Sierpinski Gasket Networks

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Analysis in Theory and Applications 2024年第1期40卷 1-21页

作者： Zhizhuo Zhang Bo Wu Zuguo Yu School of Mathematics Southeast UniversityNanjingJianagsu 211189China School of Applied Mathematics Nanjing University of Finance and EconomicsNanjingJiangsu 210023China Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education and Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtanHunan 411105China

The random walk is one of the most basic dynamic properties of complex networks,which has gradually become a research hotspot in recent years due to its many applications in actual *** important characteristic of the random walk is the mean time to absorption,which plays an extremely important role in the study of topology,dynamics and practical application of complex *** the mean time to absorption on the regular iterative self-similar network models is an important way to explore the inﬂuence of self-similarity on the properties of random walks on the *** existing literatures have proved that even local self-similar structures can greatly affect the properties of random walks on the global network,but they have failed to prove whether these effects are related to the scale of these self-similar *** this article,we construct and study a class of Horizontal Par-titioned Sierpinski Gasket network model based on the classic Sierpinski gasket net-work,which is composed of local self-similar structures,and the scale of these structures will be controlled by the partition coefﬁcient ***,the analytical expressions and approximate expressions of the mean time to absorption on the network model are obtained,which prove that the size of the self-similar structure in the network will directly restrict the inﬂuence of the self-similar structure on the properties of random walks on the ***,we also analyzed the mean time to absorption of different absorption nodes on the network toﬁnd the location of the node with the highest absorption efﬁciency.

关键词： Mean time to absorption self-similar network Sierpinski Gasket

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Asymptotic stability of many numerical schemes for phase-field modeling

arXiv

引用

arXiv 2024年

作者： Li, Pansheng Wang, Dongling Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

The numerical stability of nonlinear equations has been a long-standing concern and there is no standard framework for analyzing long-term qualitative behavior. In the recent breakthrough work [XX23], a rigorous numerical analysis was conducted on the numerical solution of a scalar ODE containing a cubic polynomial derived from the Allen-Cahn equation. It was found that only the implicit Euler method converge to the correct steady state for any given initial value u0 under the unique solvability and energy stability. But all the other commonly used second-order numerical schemes exhibit sensitivity to initial conditions and may converge to an incorrect equilibrium state as tn → ∞. This indicates that energy stability may not be decisive for the long-term qualitative correctness of numerical solutions. We found that using another fundamental property of the solution, namely monotonicity instead of energy stability, is sufficient to ensure that many common numerical schemes converge to the correct equilibrium state. This leads us to introduce the critical step size constant h∗ = h∗(u0, ϵ) that ensures the monotonicity and unique solvability of the numerical solutions, where the scaling parameter ϵ ∈ (0, 1.. For a given numerical method, if the initial value u0 is given, no matter how large it is, we prove that h∗ > 0. As long as the actual simulation step 0 ∗, the numerical solution preserves monotonicity and converges to the correct equilibrium state. On the other hand, we prove that the implicit Euler scheme h∗ = h∗(ϵ), which is independent of u0 and only depends on ϵ. Hence regardless of the initial value taken, the simulation can be guaranteed to be correct when h ∗. But for various other numerical methods, no mater how small the step size h is in advance, there will always be initial values that cause simulation errors. In fact, for these numerical methods, we prove that infu0∈R h∗(u0, ϵ) = 0. Various numerical experiments are used to confirm the theoretical anal

关键词： Nonlinear equations

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Adaptive Edge Finite Element Method and Numerical Design for Metasurface Cloak

SSRN

引用

SSRN 2023年

作者： Yang, Wei Wang, Tiancheng Mao, Jiangqiong Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

Metasurfaces are a type of metamaterial that have two-dimensional structures. In comparison to traditional metamaterials, metasurfaces have several advantages such as being lightweight, easily controllable, and simple to design. This paper outlines the phase matching principle and constitutive parameter theory of electromagnetic (EM) metasurfaces, as well as the constitutive parameter analysis and model equations for metasurface cloaks. Due to the singularity of metasurface cloaks, an adaptive edge finite element method (AEFEM) is developed in this paper. Additionally, the convergence theory of time-harmonic Maxwell’s equations for metasurface cloak is established under the T-coercivity assumption. The numerical simulations of arc-shaped metasurface cloaks have confirmed the accuracy of our model and numerical theory. Furthermore, we have utilized our numerical method to design a triangular-shaped metasurface cloak with fewer singularities. © 2023, The Authors. All rights reserved.

关键词： Maxwell equations

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