共查询到20条相似文献,搜索用时 0 毫秒
1.
研究非线性Sobolev方程Galerkin解法的后处理与超收敛.对半离散及全离散格式,证明了当有限元空间次数,r≥2时,有限元解经过后处理,H1-模和L2-模误差估计可分别提高一阶. 相似文献
2.
Nonlinear Galerkin methods are new schemes for integrating dissipative systems:In the present paper, we obtain the estimates to the rate of convergence of such methods for Kuramoto-Sivashinsky equations. In particular, by an illustrative example, we show that nonlinear Galerkin methods converge faster than the usual Galerkin method. 相似文献
3.
Guo Boling 《数学年刊B辑(英文版)》1995,16(3):379-390
NONLINEARGALERKINMETHODSFORSOLVINGTWODIMENSIONALNEWTON-BOUSSINESQEQUATIONS¥GUOBOLINGAbstract:ThenonlinearGalerkinmethodsforso... 相似文献
4.
本文给出了数值求解非线性发展方程的全离散非线性Galerkin算法,即将空间离散时的谱非线性Galerkin算法和时间离散的Euler差分格式相结合,得到了显式和隐式两种全离散数值格式,相应地也考虑了显式和隐式的Galerkin全离散格式,并分别分析了上述四种全离散格式的收敛性和复杂性,经过比较得出结论;在某些约束条件下,非线性Galerkin算法和Galerkin算法具有相同阶的收敛速度,然而前 相似文献
5.
求解非线性方程的双函数法 总被引:15,自引:0,他引:15
基于齐次平衡法和李志斌的tanh函数法,得到简单有效的求解非线性发展方程的双函数法,这种方法利用非线性发展方程孤立波的局部性特点,把非线性方程的孤波解表示为函数f和g的多项式,并用这种方法求出了非线性波理论中的基本模型KdV方程的多组孤波解。 相似文献
6.
I Let D be a launder domain in Rz with Lipehitz continuous bodare I'. ac consider the stream-vortidty form of hmedependent Navier-stokes Muahons describing the 'flow Of a ~ incompreSSible nuid confined in Dwhere to and & are vorticity and stream function. BecaUSe the action (1) doeS not include the differentialten z, ~ tie ~ con&tion of' dab at In tthe Paper, we give a ho element n~ Galerkin ~, acs ~ is ~ an tab finite element spaceS X. and X* for the aPPmxhaation of the ~ ac v~ fUncti… 相似文献
7.
一类非线性发展方程初边值问题解的Blow—up 总被引:3,自引:1,他引:2
杨志坚 《高校应用数学学报(A辑)》1993,(4):351-359
本文利用Fourier变换方法,研究了一类非线性拟双曲方程的初边值问题的解的bolw-up问题,并给出了其解在有限时间内bolw-up的条件。 相似文献
8.
1.Introduction'NonlinearGalerkinmethodisnumericalmethodfordissipativeevolutionpartialdifferentialequationswherethespatialdiscretizationreliesonanonlinearmanifoldinsteadofalinearspaceasintheclassicalGalerkinmethod.Morepreciselygoneconsidersafinitedimension… 相似文献
9.
1. IntroductionIn the numerical simulation of the Navier-Stokes equations one encounters three seriousdifficulties in the case of large Reynolds numbers f the treatment of the incomPressibility con-dition divu = 0, the treatment of the noIilinear terms and the large time integration. For thetreatment of the incoInPressibility condition, one use the penalty method in the case of finiteelemellts [1--2l and for the treatmen of the noulinar terms and the large tfor integration, oneuse the nonlin… 相似文献
10.
Yu-jiang wu 《计算数学(英文版)》1999,17(3):243-256
1.IntroductionThenonlinearGalerkinmethodwasintroducedbyMarionandTemaml4],whichisstemmedfromthetheoryofinertialmanifoldsanddynamicalsystemtheory.The'considerableincreaseinthecomputingpowerduringlastyearsmakesitpossibleforthemathematicianstosolvenumeri... 相似文献
11.
一类非线性发展方程的精确孤波解 总被引:4,自引:1,他引:4
张卫国 《高校应用数学学报(A辑)》1996,(4):399-408
本文首先求出了非线性常微分方程u″(ξ)+mu2(ξ)+nu3(ξ)+pu(ξ)=c(Ⅰ)和u″(ξ)+ru′(ξ)+mu2(ξ)+nu3(ξ)+pu(ξ)=c(Ⅱ)的显式精确解.进而求出了组合BBM方程、Burgers方程与组合BBM方程混合型的钟状孤波解和扭状孤波解,同时还求出了广义Boussinesq方程和广义KP方程的钟状和扭状孤波解.文中指出了其行波解可化为(Ⅰ)的发展方程既有钟状又有扭状孤波解,而其行波解可化为(Ⅱ)的发展方程没有钟状孤波解. 相似文献
12.
1.IntroductionNonlinearGalerkinmethodsaremultilevelschemesforthedissipativeevolutionpartialdifferentialequations.Theycorrespondtothesplittingsoftheunknownu:u=y z)wherethecomponentsareofdifferentorderofmagnitudewithrespecttoaparameterrelatedtothespati... 相似文献
13.
本文利用间断有限元法求解非线性延迟微分方程,在拟等级网格下.给出非线性延迟微分方程间断有限元解的整体收敛阶和局部超收敛阶,数值实验验证了理论结果的正确性. 相似文献
14.
This paper is concerned with developing accurate and efficient numerical methods for one-dimensional fully nonlinear second order elliptic and parabolic partial differential equations (PDEs). In the paper we present a general framework for constructing high order interior penalty discontinuous Galerkin (IP-DG) methods for approximating viscosity solutions of these fully nonlinear PDEs. In order to capture discontinuities of the second order derivative uxx of the solution u, three independent functions p1,p2 and p3 are introduced to represent numerical derivatives using various one-sided limits. The proposed DG frame- work, which is based on a nonstandard mixed formulation of the underlying PDE, embeds a nonlinear problem into a mostly linear system of equations where the nonlinearity has been modified to include multiple values of the second order derivative uxz. The proposed framework extends a companion finite difference framework developed by the authors in [9] and allows for the approximation of fully nonlinear PDEs using high order polynomials and non-uniform meshes. In addition to the nonstandard mixed formulation setting, another main idea is to replace the fully nonlinear differential operator by a numerical operator which is consistent with the differential operator and satisfies certain monotonicity (called g-monotonicity) properties. To ensure such a g-monotonicity, the crux of the construction is to introduce the numerical moment, which plays a critical role in the proposed DG frame- work. The g-monotonicity gives the DG methods the ability to select the mathematically "correct" solution (i.e., the viscosity solution) among all possible solutions. Moreover, the g-monotonicity allows for the possible development of more efficient nonlinear solvers as the special nonlinearity of the algebraic systems can be explored to decouple the equations. This paper also presents and analyzes numerical results for several numerical test problems which are used to guage the accuracy and efficiency of the proposed DG methods. 相似文献
15.
1.引言对于Navier-Stokes方程有限元数值求解方面的研究已有很多的文章和专著,多数是采用有限元Galerkin算法,例见文献[1-4].然而,由于Navier-Stokes方程在大雷诺数时有其强的非线性性和对时间土的长期依赖性,用计算机求解Navier-Stokes方程在速度和容量方面是难以承受的.为了克服这些困难,最近人们提出了有限元非线性Galerkin算法,见文献卜8],然而这种算法只是在某一有限时刻之后具有好的收敛速度,在初始时刻的某一区间不能达到好的收敛速度.本文应用Taylor展开技术导出了数值求解二维非定常Navier-Stokes方程的最佳… 相似文献
16.
In this paper,we provide a number of new estimates on the stability and convergence of both hybrid discontinuous Galerkin(HDG)and weak Galerkin(WG)methods.By using the standard Brezzi theory on mixed methods,we carefully define appropriate norms for the various discretization variables and then establish that the stability and error estimates hold uniformly with respect to stabilization and discretization parameters.As a result,by taking appropriate limit of the stabilization parameters,we show that the HDG method converges to a primal conforming method and the WG method converges to a mixed conforming method. 相似文献
17.
18.
本文给出了二维非定常N-S方程的三种数值格式,其中空间变量用谱非线性Galerkin算法进行离散,时间变量用有限差分离散,并研究了这些格式数值解的逼近精度.最后,给出了部分数值计算结果. 相似文献
19.
两类变时间步长的非线性Galerkin算法的稳定性 总被引:3,自引:0,他引:3
1.引言近年来,随着计算机的飞速发展,人们越来越关心非线性发展方程解的渐进行为.为了较精确地描述解在时间t→∞时的渐进行为,人们发展了一类惯性算法,即非线性Galerkin算法.该算法是将来解空间分解为低维部分和高维部分,相应的方程可以分别投影到它们上面,它的解也相应地分解为两部分,大涡分量和小涡分量;然后核算法给出大涡分量和小涡分量之间依赖关系的一种近似,以便容易求出相应的近似解.许多研究表明,非线性Galerkin算法比通常的Galerkin算法节省可观的计算量.当数值求解微分方程时,计算机只能对已知数据进行有限位… 相似文献
20.
本文利用林群教授[4]介绍的有限元方法,对藕合半线性问题做后处理,使整体解超一阶收敛. 相似文献