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定常的Navier-Stokes方程的非线性Galerkin混合元法及其后验估计 总被引:1,自引:1,他引:0
提出了定常的Navier-Stokes方程的一种非线性Galerkin混合元法,并导出非线性Galerkin混合元解的存在性和误差估计及其后验误差估计. 相似文献
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研究三维非线性抛物型积分-微分方程的A.D.I.Galerkin方法.通过交替方向,化三维为一维,简化计算;通过Galerkin法,保持高精度.成功处理了Volterra项的影响;对所提Galerkin及A.D.I.Galerkin格式给出稳定性和收敛性分析,得到最佳H1和L2模估计. 相似文献
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非线性Galerkin方法是对耗散型非线性发展方程的一种数值解法,其空间变量不象一般Galerkin方法那样在线性空间上离散,而是在非线性流形上离散,所得逼近解在时间变量增大时可以更快地逼近其精确解.精细的理论分析可见[1],[2]等,在有限元逼近基础上将此方法应用到Navier-Stokes方程上的工作可参见[3],[4],这些文章主要针对速度与压力同时求解的混合元情形做了讨论.本文在[4]的基础上对加罚Navier-Stokes方程的一种非线性Galerkin方法的半离散和全离散有限元逼近格式分别进行了误差估 相似文献
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提出了求解时间分数阶对流-扩散方程的局部间断Galerkin谱方法.在空间方向上,按局部间断Galerkin谱方法进行离散,时间方向上,对α阶Caputo时间分数阶导数按有限差分格式进行离散,非线性项和源项采用Chebyshev-Gauss-Lobatto插值,从而得到有限差分/局部间断Galerkin谱全离散格式,并且给出了其全离散格式线性情形下的稳定性和收敛性分析.最后给出了一些数值算例,比较了单区域方法和局部间断Galerkin谱方法的数值结果,得出后种方法更具优势.还通过对比Gorenflo-Mainardi-Moretti-Paradisi(GMMP)和有限差分这两种全离散格式下的数值结果,得出有限差分格式在某些问题中比GMMP格式精度更高,收敛速度更快. 相似文献
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加罚N-S方程的有限元非线性Galerkin方法 总被引:4,自引:2,他引:4
非线性Galerkin方法是对耗散型非线性发展方程的一种数值解法,其空间变量不象一般Galerkin方法那样在线性空间上离散,而是在非线性流形上离散,所得逼近解在时间变量增大时可以更快地逼近其精确解.精细的理论分析可见[1],[2]等,在有限元逼近基础上将此方法应用到Navier-Stokes方程上的工作可参见[3],[4],这些文章主要针对速度与压力同时求解的混合元情形做了讨论.本文在[4]的基础上对加罚Navier-Stokes方程的一种非线性Galerkin方法的半离散和全离散有限元逼近格式分别进行了误差估 相似文献
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《数学的实践与认识》2018,(23)
提出一种求解非线性扩散方程的直接间断Galerkin方法.在空间离散上,采用Stirling插值公式构造了一种含有高阶导数项的数值流;在时间离散上,采用通常的Runge-Kutta方法.在理论上,证明了由这种直接间断Galerkin方法得到的计算格式是非线性稳定的,相应数值解不仅具有最优的能量误差估计,而且具有最优的L~2误差估计.数值实验验证了方法的有效性. 相似文献
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提出了积分非线性发展方程的新方法,即Taylor展开方法.标准的Galerkin方法可以看作0-阶Taylor展开方法,而非线性Galerkin方法可以看作1-阶修正Taylor展开方法A·D2此外,证明了数值解的存在性及其收敛性.结果表明,在关于严格解的一些正则性假设下,较高阶的Taylor展开方法具有较高阶的收敛速度.最后,给出了用Taylor展开方法求解二维具有非滑移边界条件Navier-Stokes方程的具体例子. 相似文献
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We introduce some variations of the interval Newton method for bounding solutions to a set ofn nonlinear equations. It is pointed out that previous implementations of Krawczyk's method are very inefficient and an improved version is given. A superior type of Newton method is introduced. 相似文献
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In this work, an improved version of the fractional variational iteration method is presented, for solving fractional initial value problems. The nonlinear terms of fractional differential equations are linearized via the famous Adomian series. The fractional differential functions are employed in the numerical simulation. Two examples are given as illustrations. 相似文献
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Tudor Barbu 《Numerical Functional Analysis & Optimization》2013,34(11):1375-1387
In this article we consider a novel nonlinear PDE-based image denoising technique. The proposed restoration model uses second-order hyperbolic diffusion equations. It represents an improved nonlinear version of a linear hyperbolic PDE model developed recently by the author, providing more effective noise removal results while preserving the edges and other image features. A rigorous mathematical investigation is performed on this new differential model and its well-posedness is treated. Next, a consistent finite-difference numerical approximation scheme is proposed for this nonlinear diffusion-based approach. Our successful image denoising experiments and method comparisons are also described. 相似文献
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Rizwan-uddin 《Numerical Methods for Partial Differential Equations》1997,13(2):113-145
An improved variation of the nodal integral method to solve partial differential equations has been developed and implemented. Rather than treating all of the nonlinear terms as the so-called pseudo-source terms (to be approximated), in this modified version of the nodal integral method, by approximating part of the nonlinear terms in terms of the discrete variable(s) that ultimately result at the end of the formulation process, some or all of the nonlinear terms are kept on the left-hand side in the transverse-integrated equations, which are to be solved analytically. Application of the method to solve the Burgers equation leads to exponential variation within the nodes and shows that the resulting scheme has inherent upwinding. Reconstruction of node interior solution—as a function of one independent variable, and averaged in all others—makes it possible to obtain rather accurate solutions even on a fine scale. Results of the numerical analysis and comparison with results of other methods reported in the literature show that the new method is comparable and sometimes better in accuracy than the currently used schemes. Extension to multidimensional, time-dependent problems is straightforward. © 1997 John Wiley & Sons, Inc. 相似文献
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改进了奇异非线性边值问题的经典Agarwal-O'Regan方法.利用这个改进的方法建立了奇异非线性(p,n-p)共轭边值问题正解的局部存在性与多解性,其中允许非线性项关于时间和空间变元同时奇异.主要工具是锥拉伸与锥压缩型的Guo-Krasnosel'skii不动点定理和精确先验估计技巧.特别的,考察了非自治奇异非线性二阶、三阶、四阶共轭边值问题. 相似文献
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Periodic homogenization of strongly nonlinear reaction–diffusion equations with large reaction terms
Nils Svanstedt 《Applicable analysis》2013,92(7):1357-1378
We study in this article the periodic homogenization problem related to a strongly nonlinear reaction–diffusion equation. Owing to the large reaction term, the homogenized equation has a rather quite different form which puts together both the reaction and convection effects. We show in a special case that the homogenized equation is exactly of a convection-diffusion type. This study relies on a suitable version of the well-known two-scale convergence method. 相似文献
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We solve the problem of describing all nonsingular pairs of compatible flat metrics (or, in other words, nonsingular flat pencils of metrics) in the general N-component case. This problem is equivalent to the problem of describing all compatible Dubrovin–Novikov brackets (compatible nondegenerate local Poisson brackets of hydrodynamic type) playing an important role in the theory of integrable systems of hydrodynamic type and also in modern differential geometry and field theory. We prove that all nonsingular pairs of compatible flat metrics are described by a system of nonlinear differential equations that is a special nonlinear differential reduction of the classical Lamé equations, and we present a scheme for integrating this system by the method of the inverse scattering problem. The integration procedure is based on using the Zakharov method for integrating the Lamé equations (a version of the inverse scattering method). 相似文献
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Error analysis of upwind‐discretizations for the steady‐state incompressible Navier–Stokes equations
Lutz Angermann 《Advances in Computational Mathematics》2000,13(2):167-198
Within the framework of finite element methods, the paper investigates a general approximation technique for the nonlinear
convective term of the Navier–Stokes equations. The approach is based on an upwind method of finite volume type. It is proved
that the discrete convective term satisfies a well‐known collection of sufficient conditions for convergence of the finite
element solution.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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Ya Xu Bingsheng He Xiaoming Yuan 《Journal of Mathematical Analysis and Applications》2006,322(1):276-287
Inspired by the Logarithmic-Quadratic Proximal method [A. Auslender, M. Teboulle, S. Ben-Tiba, A logarithmic-quadratic proximal method for variational inequalities, Comput. Optim. Appl. 12 (1999) 31-40], we present a new prediction-correction method for solving the nonlinear complementarity problems. In our method, an intermediate point is produced by approximately solving a nonlinear equation system based on the Logarithmic-Quadratic Proximal method; and the new iterate is obtained by convex combination of the previous point and the one generated by the improved extragradient method at each iteration. The proposed method allows for constant relative errors and this yields a more practical Logarithmic-Quadratic Proximal type method. The global convergence is established under mild conditions. Preliminary numerical results indicate that the method is effective for large-scale nonlinear complementarity problems. 相似文献
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Maria Rosaria Capobianco Giuliana Criscuolo Peter Junghanns 《Numerical Algorithms》2010,55(2-3):205-221
Different iterative schemes based on collocation methods have been well studied and widely applied to the numerical solution of nonlinear hypersingular integral equations (Capobianco et al. 2005). In this paper we apply Newton’s method and its modified version to solve the equations obtained by applying a collocation method to a nonlinear hypersingular integral equation of Prandtl’s type. The corresponding convergence results are derived in suitable Sobolev spaces. Some numerical tests are also presented to validate the theoretical results. 相似文献