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APPROXIMATION OF NONCONFORMING QUASI-WILSON ELEMENT FOR sine-gordon equations

Journal of Computational Mathematics 2013年第3期31卷 271-282页

作者： Dongyang Shi Ding Zhang Department of Mathematics Zhengzhou University Zhengzhou 450001 China School of Mathematics and Statistics Xuchang University Xuehang 461000 China

In this paper, nonconforming quasi-Wilson finite element approximation to a class of nonlinear sine-Gordan equations is discussed. Based on the known higher accuracy results of bilinear element and different techniques from the existing literature, it is proved that the inner product △↓（u - Ih^1u）, △↓vh） and the consistency error can be estimated as order O（h^2） in broken H^1 - norm/L^2 - norm when u ∈ H^3（Ω）/H^4（Ω）, where Ih^1u is the bilinear interpolation of u, Vh belongs to the quasi-Wilson finite element space. At the same time, the superclose result with order O（h^2） for semi-discrete scheme under generalized rectangular meshes is derived. Furthermore, a fully-discrete scheme is proposed and the corresponding error estimate of order O（h^2 ＋ τ^2） is obtained for the rectangular partition when u ∈ H^4（Ω）, which is as same as that of the bilinear element with ADI scheme and one order higher than that of the usual analysis on nonconforming finite elements.

关键词： sine-gordon equations Quasi-Wilson element Semi-discrete and fully-discrete schemes Error estimate and superclose result.

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SYMPLECTIC SCHEMES FOR QUASILINEAR WAVE equations OF KLEIN-gordon AND sine-gordon TYPE

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Journal of Computational Mathematics 2001年第5期19卷 475-488页

作者： Xiao-wu Lu (Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA) Emory University 美国 30322

Presents a class of finite difference methods of first and second order accuracy for the computation of solutions to the quasilinear wave equations. Overview of general symplectic schemes and generating functional; Nu... 详细信息

关键词： Symplectic integration sine-gordon equations Finite difference method.

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A numerical method for one-dimensional nonlinear sine-gordon equation using multiquadric quasi-interpolation

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Chinese Physics B 2009年第8期18卷 3099-3103页

作者：马利敏吴宗敏 Shanghai Key Laboratory for Contemporary Applied Mathematics School of Mathematical SciencesFudan University

In this paper, we use a univariate multiquadric quasi-interpolation scheme to solve the one-dimensional nonlinear sine-gordon equation that is related to many physical phenomena. We obtain a numerical scheme by using the derivative of the quasi-interpolation to approximate the spatial derivative and a difference scheme to approximate the temporal derivative. The advantage of the obtained scheme is that the algorithm is very simple so that it is very easy to implement. The results of numerical experiments are presented and compared with analytical solutions to confirm the good accuracy of the presented scheme.

关键词： quasi-interpolation Hardy Multiquadric (MQ) interpolation methods sine-gordon equations scattered data approximation meshless method

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