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BOUNDARY PENALTY finite element methods FOR BLENDING SURFACES,I BASIC THEORY

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Journal of Computational Mathematics 1998年第5期16卷 457-480页

作者： Zi-cai Li (Department of Applied Mathematics, National Sun Yat-sen University,Kaohsiung 80242, Taiwan) National Sun Yat-sen Univerisy 台湾

When parametric functions are used to blend 3D surfaces, geometric continuity of displacements and derivatives until to the surface boundary must be satisfied. By the traditional blending techniques, however, arbitrariness of the solutions arises to cause a difficulty in choosing a suitable blending surface. Hence to explore new blending techniques is necessary to construct good surfaces so as to satisfy engineering requirements. In this paper, a blending surface is described as a flexibly elastic plate both in partial differential equations and in their variational equations, thus to lead to a unique solution in a sense of the minimal global surface curvature. Boundary penalty finite element methods (BP-FEMs) with and without approximate integration are proposed to handle the complicated constraints along the blending boundary. Not only have the optimal convergence rate O(h(2)) of second order generalized derivatives of the solutions in the solution domain been obtained, but also the high convergence rate O(h(4)) of the tangent boundary condition of the solutions can be achieved, where h is the maximal boundary length of rectangular elements used. Moreover, useful guidance in computation is discovered to deal with interpolation and approximation in the boundary penalty integrals. A numerical example is also provided to verify perfectly the main theoretical analysis made. This paper yields a framework of mathematical modelling, numerical techniques and error analysis to the general and complicated blending problems.

关键词： blending surfaces parametric surfaces plate mathematical modelling variational equations finite element methods boundary penalty method computer geometric aided design

STABILITY ANALYSIS OF finite element methods FORTHE ACOUSTIC WAVE EQUATION WITH ABSORBINGBOUNDARY CONDITIONS (PART I)

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Journal of Computational Mathematics 1999年第3期17卷 293-306页

作者： Xiu-min Shao Zhi-ling Lan(Institute of Mathematics, Academy of Sciences, Beijing 100080, China) 中科院数学所北京

In Part I and Part II of this paper initial-boundary value problems of the acoustic wave equation with absorbing boundary conditions are considered. Their finite element-finite difference computational schemes are proposed. The stability of the schemes is discussed and the corresponding stability conditions are given. Part I and Part II concern the first- and the second-order absorbing boundary conditions, respectively. Finally, numerical results are presented in Part II to show the correctness of theoretical analysis. (Author abstract) 7 Refs.

关键词： stability finite element methods wave equation absorbing boundary conditions

ASYMPTOTICAL STABILITY OF NEUTRAL REACTION-DIFFUSION EQUATIONS WITH PCAS AND THEIR finite element methods

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Acta Mathematica Scientia 2023年第4期43卷 1865-1880页

作者：韩豪张诚坚 School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China

This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous ***,for the analytical solutions of the equations,we derive their expressions and asymptotical stability ***,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically ***,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.

关键词： neutral reaction-diffusion equations piecewise continuous arguments asymptotical stability finite element methods numerical experiment

IMPLICIT-EXPLICIT MULTISTEP finite element-MIXED finite element methods FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

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Acta Mathematica Scientia 2003年第3期23卷 386-398页

作者：陈蔚 Academy of Mathematics System science CASBeijing 100080China School of EconomicsShandong UniversityJinan 250100China

The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density. The electric potential equation is discretized by a mixed finite element method. The electron and hole density equations are treated by implicit-explicit multistep finite element methods. The schemes are very efficient. The optimal order error estimates both in time and space are derived.

关键词： Semiconductor device strongly A(0)-stable multistep methods finite element methods mixed finite element methods

RICHARDSON EXTRAPOLATION AND DEFECT CORRECTION OF finite element methods FOR OPTIMAL CONTROL PROBLEMS

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Journal of Computational Mathematics 2010年第1期28卷 55-71页

作者： Tang Liu Ningning Yan Shuhua Zhang Research Center for Mathematics and Economics Tianjin University of Finance and Economics Tianjin 300222 China Institute of System Sciences Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100190 China

Asymptotic error expansions in H^1-norm for the bilinear finite element approximation to a class of optimal control problems are derived for rectangular meshes. With the rectan- gular meshes, the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied. The higher order numerical approximations are used to generate a posteriori error estimators for the finite element approximation.

关键词： Optimal control problem finite element methods Asymptotic error expansions Defect correction A posteriori error estimates.

A Priori Error Estimates of finite element methods for Linear Parabolic Integro-Differential Optimal Control Problems

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Advances in Applied Mathematics and Mechanics 2014年第5期6卷 552-569页

作者： Wanfang Shen Liang Ge Danping Yang Wenbin Liu School of Mathematic and Quantitative Economics Shandong University of Finance and EconomicsJinan 250014China Shandong Provincial Key Laboratory of Computer Network Shandong Computer Science CenterJinan 250014China Department of Mathematics East China Normal UniversityShanghai 200241China KBS University of KentCanterburyCT27NFEngland

In this paper,we study the mathematical formulation for an optimal control problem governed by a linear parabolic integro-differential equation and present the optimality *** then set up its weak formulation and the finite element approximation *** on these we derive the a priori error estimates for its finite element approximation both in H1 and L^(2)*** some numerical tests are presented to verify the theoretical results.

关键词： Optimal control linear parabolic integro-differential equations optimality conditions finite element methods a priori error estimate.

A Posteriori Error Estimates for finite element methods for Systems of Nonlinear,Dispersive Equations

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Communications on Applied Mathematics and Computation 2022年第3期4卷 823-854页

作者： Ohannes A.Karakashian Michael M.Wise Department of Mathematics University of TennesseeKnoxvilleTNUSA Advanced Technology Integration Department DyneticsInc.HuntsvilleALUSA

The present study regards the numerical approximation of solutions of systems of Korteweg-de Vries type,coupled through their nonlinear *** our previous work[9],we constructed conservative and dissipative finite element methods for these systems and presented a priori error estimates for the semidiscrete *** this sequel,we present a posteriori error estimates for the semidiscrete and fully discrete approximations introduced in[9].The key tool employed to effect our analysis is the dispersive reconstruction devel-oped by Karakashian and Makridakis[20]for related discontinuous Galerkin *** conclude by providing a set of numerical experiments designed to validate the a posteriori theory and explore the effectivity of the resulting error indicators.

关键词： finite element methods Discontinuous Galerkin methods Korteweg-de Vries equation A posteriori error estimates Conservation laws Nonlinear equations Dispersive equations

Moving finite element methods for a System of Semi-Linear Fractional Diffusion Equations

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Advances in Applied Mathematics and Mechanics 2016年第6期8卷 911-931页

作者： Jingtang Ma Zhiqiang Zhou School of Economic Mathematics Southwestern University of Finance and EconomicsChengdu 611130China

This paper studies a system of semi-linear fractional diffusion equations which arise in competitive predator-preymodels by replacing the second-order derivatives in the spatial variables with fractional derivatives of order less than *** finite element methods are proposed to solve the system of fractional diffusion equations and the convergence rates of the methods are *** examples are carried out to confirm the theoretical *** applications in anomalous diffusive Lotka-Volterra and Michaelis-Menten-Holling predator-preymodels are studied.

关键词： finite element methods fractional differential equations predator-preymodels

Electrode Design of Cylindrical Coplanar-grid CdZnTe Detector by finite element methods

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Semiconductor Photonics and Technology 2004年第1期10卷 48-52页

作者： JINWei SANGWen-bin ZHANGQi MINJia-Hua SHENYan Dept.ofMater.Sci.andEng. ShanghaiUniversityShanghai201800CHN

Cylindrical coplanar-grid configurations,which offer a lot of advantages over established designs,can effectively overcome the problem of poor hole *** element analysis is utilized for simulating the potential distribution of the cylindrical coplanar-grid detector under different models by varying the widths of grid and pitch of electrodes. In addition, a modified grid pattern has been discussed to improve the weighting potential match between two grids. In this way, the geometry of electrodes for cylindrical coplanar-grid detectors is optimized.

关键词： CdZnTe finite element methods Coplanar-grid Detector