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Convergence and error estimate of cascade algorithms with infinitely supported masks in L_p(R^s)

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Science China Mathematics 2012年第3期55卷 577-592页

作者： YANG JianBin LI Song Department of Mathematics College of Sciences Hohai University Nanjing 210098 China Department of Mathematics College of Sciences Zhejiang University Hangzhou 310027 China

The cascade algorithm plays an important role in computer graphics and wavelet *** this paper,we first investigate the convergence of cascade algorithms associated with a polynomially decaying mask and a general dilation matrix in L p (R s) (1 p ∞) spaces,and then we give an error estimate of the cascade algorithms associated with truncated *** is proved that under some appropriate conditions if the cascade algorithm associated with a polynomially decaying mask converges in the L p-norm,then the cascade algorithms associated with the truncated masks also converge in the L ***,the error between the two resulting limit functions is estimated in terms of the masks.

关键词： cascade algorithm polynomially decaying masks error estimate

error estimate of Full-Discrete Numerical Scheme for the Nonlocal Allen-Cahn Model

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Journal of Mathematical Research with Applications 2024年第3期44卷 344-358页

作者： Jun ZHANG Xiaohu YANG Fulin MEI Zhimei JI Yu ZHANG School of Mathematics and Statistics Guizhou University of Finance and Economics The Meteorological Disaster Prevention Center of Guizhou Province Xi'an Institute of Applied Optics Financial Department Guizhou University of Finance and Economics

In this work, we study the error estimates of the fully discrete Fourier pseudospectral numerical scheme for solving the nonlocal volume-conserved Allen-Cahn(AC) *** time marching method of the numerical scheme is based on the well-known Invariant Energy Quadratization(IEQ) method. We demonstrate that the proposed fully discrete numerical method is uniquely solvable, unconditionally energy stable, and obtain the optimal error estimate of the scheme for both space and time. Additionally, we conduct several numerical tests to verify the theoretical results.

关键词： nonlocal Allen-Cahn model uniquely solvable unconditionally energy stable error estimate numerical tests

A new a priori error estimate of nonconforming finite element methods

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Science China Mathematics 2014年第5期57卷 887-902页

作者： HU Jun MA Rui1 SHI ZhongCi LMAM and School of Mathematical Sciences Peking University LSEC ICMSECAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

This paper is devoted to a new error analysis of nonconforming finite element *** with the classic error analysis in literature,only weak continuity,the F-E-M-Test for nonconforming finite element spaces,and basic Hm regularity for exact solutions of 2m-th order elliptic problems under consideration are *** analysis is motivated by ideas from a posteriori error estimates and projection average *** main ingredient is a novel decomposition for some key average terms on(n.1)-dimensional faces by introducing a piecewise constant projection,which defines the generalization to more general nonconforming finite elements of the results in *** analysis and results herein are conjectured to apply for all nonconforming finite elements in literature.

关键词： nonconforming finite element consistency error error estimate

On the error estimate of Adini's Element for the Second Order Problems

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Chinese Quarterly Journal of Mathematics 2007年第3期22卷 364-369页

作者：高继梅李文华 Department of Mathematics Zhoukou Normal College Department of Mathematics Zhengzhou University

The main aim of this paper is to have an accurate analysis on the famous Adini＇s element for the second order problems under to the anisotropic meshes. We firstly show that the interpolation of Adini＇s element satisfy the anisotropic property. Then the optimal error estimate is obtained without the regularity assumption on the meshes.

关键词： Adini's element anisotropic regularity assumption error estimate

error estimateS FOR TWO-SCALE COMPOSITE FINITE ELEMENT APPROXIMATIONS OF NONLINEAR PARABOLIC EQUATIONS

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Journal of Computational Mathematics 2021年第4期39卷 493-517页

作者： Tamal Pramanick Department of Mathematics National Institute of Technology CalicutKozhikode-673601India

We study spatially semidiscrete and fully discrete two-scale composite nite element method for approximations of the nonlinear parabolic equations with homogeneous Dirichlet boundary conditions in a convex polygonal domain in the *** new class of nite elements,which is called composite nite elements,was rst introduced by Hackbusch and Sauter[***.,75(1997),pp.447-472]for the approximation of partial di erential equations on domains with complicated *** aim of this paper is to introduce an effcient numerical method which gives a lower dimensional approach for solving partial di erential equations by domain discretization *** composite nite element method introduces two-scale grid for discretization of the domain,the coarse-scale and the ne-scale grid with the degrees of freedom lies on the coarse-scale grid *** the ne-scale grid is used to resolve the Dirichlet boundary condition,the dimension of the nite element space depends only on the coarse-scale *** a consequence,the resulting linear system will have a fewer number of unknowns.A continuous,piecewise linear composite nite element space is employed for the space discretization whereas the time discretization is based on both the backward Euler and the Crank-Nicolson *** have derived the error estimates in the L^(∞)(L^(2))-norm for both semidiscrete and fully discrete ***,numerical simulations show that the proposed method is an efficient method to provide a good approximate solution.

关键词： Composite nite elements Nonlinear parabolic problems Coarse-scale Finescale Semidiscrete Fully discrete error estimate

CONVERGENCE OF AN IMMERSED INTERFACE UPWIND SCHEME FOR LINEAR ADVECTION EQUATIONS WITH PIECEWISE CONSTANT COEFFICIENTS I:L^1-error estimateS

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Journal of Computational Mathematics 2008年第1期26卷 1-22页

作者： Xin Wen Shi Jin LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China Department of Mathematics University of Wisconsin Madison WI 53706 USAand Department of Mathematical Sciences Tsinghua University Beijing 100084 China

We study the L^l-error estimates for the upwind scheme to the linear advection equations with a piecewise constant coefficients modeling linear waves crossing interfaces. Here the interface condition is immersed into the upwind scheme. We prove that, for initial data with a bounded variation, the numerical solution of the immersed interface upwind scheme converges in L^l-norm to the differential equation with the corresponding interface condition. We derive the one-halfth order L^l-error bounds with explicit coefficients following a technique used in [25]. We also use some inequalities on binomial coefficients proved in a consecutive paper [32].

关键词： Linear advection equations Immersed interface upwind scheme Piecewise constant coefficients error estimate Half order error bound

A POSTERIORI error estimateS IN ADINI FINITE ELEMENT FOR EIGENVALUE PROBLEMS

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Journal of Computational Mathematics 2000年第4期18卷 413-418页

作者： Yi-du Yang (Department of Mathematics, Guizhou Normal University, Guiyang, 550001) 贵州师范大学贵州贵阳 550001

In this paper, we discuss a posteriori error estimates of the eigenvalue λ[sub h] given by Adini nonconforming finite element. We give an assymptotically exact error estimator of the λ[sub h]. We prove that the order of convergence of the λ[sub h] is just 2 and the converge from below for sufficiently small h. [ABSTRACT FROM AUTHOR]

关键词： eigenvalue nonconforming finite element error estimate

Approximate Damped Oscillatory Solutions for Compound KdV-Burgers Equation and Their error estimates

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Acta Mathematicae Applicatae Sinica 2012年第2期28卷 305-324页

作者： Wei-guo ZHANG Yan ZHAO Xiao-yan TENG School of Science University of Shanghai for Science and Technology Shanghai 200093 China College of Mathematics and Physics Nanjing University of Information Science and TechnologyNanjing 210044 China College of Foundation Shanghai University of Engineering Science Shanghai 201600 China

In this paper, we focus on studying approximate solutions of damped oscillatory solutions of the compound KdV-Burgers equation and their error estimates. We employ the theory of planar dynamical systems to study traveling wave solutions of the compound KdV-Burgers equation. We obtain some global phase portraits under different parameter conditions as well as the existence of bounded traveling wave solutions. Furthermore, we investigate the relations between the behavior of bounded traveling wave solutions and the dissipation coefficient r of the equation. We obtain two critical values of r, and find that a bounded traveling wave appears as a kink profile solitary wave if │r│ is greater than or equal to some critical value, while it appears as a damped oscillatory wave if │r│is less than some critical value. By means of analysis and the undetermined coefficients method, we find that the compound KdV-Burgers equation only has three kinds of bell profile solitary wave solutions without dissipation. Based on the above discussions and according to the evolution relations of orbits in the global phase portraits, we obtain all approximate damped oscillatory solutions by using the undetermined coefficients method. Finally, using the homogenization principle, we establish the integral equations reflecting the relations between exact solutions and approximate solutions of damped oscillatory solutions. Moreover, we also give the error estimates for these approximate solutions.

关键词： compound KdV-Burgers equation qualitative analysis solitary wave solution damped oscillatorysolution error estimate

THE L1-error estimateS FOR A HAMILTONIAN-PRESERVING SCHEME FOR THE LIOUVILLE EQUATION WITH PIECEWISE CONSTANT POTENTIALS AND PERTURBED INITIAL DATA

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Journal of Computational Mathematics 2011年第1期29卷 26-48页

作者： Xin Wen LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

We study the Ll-error of a Hamiltonian-preserving scheme, developed in [19], for the Liouville equation with a piecewise constant potential in one space dimension when the initial data is given with perturbation errors. We extend the l1-stability analysis in [46] and apply the Ll-error estimates with exact initial data established in [45] for the same scheme. We prove that the scheme with the Dirichlet incoming boundary conditions and for a class of bounded initial data is Ll-convergent when the initial data is given with a wide class of perturbation errors, and derive the Ll-error bounds with explicit coefficients. The convergence rate of the scheme is shown to be less than the order of the initial perturbation error, matching with the fact that the perturbation solution can be l1-unstable.

关键词： Liouville equations Hamiltonian preserving schemes Piecewise constant po-tentials error estimate Perturbed initial data Semiclassical limit.