共查询到20条相似文献,搜索用时 31 毫秒
1.
本文讨论了mortar型旋转Q_1元的多重网格方法.证明了W循环的多重网格法是最优的,即收敛率与网格尺寸及层数无关.同时给出了一种可变的V循环多重网格算法,得到了一个条件数一致有界的预条件子.最后,数值试验验证了我们的理论结果. 相似文献
2.
In this paper we study the theoretical properties of multigrid algorithm for discretization of the Poisson equation in 2D using a mortar element method under the assumption that the triangulations on every subdomain are uniform. We prove the convergence of the W-cycle with a sufficiently large number of smoothing steps. The 相似文献
3.
CASCADIC MULTIGRID METHOD FOR THE MORTAR ELEMENT METHOD FOR P1 NONCONFORMING ELEMENT 总被引:3,自引:0,他引:3
Chun-jia Bi Dan-hui Hong 《计算数学(英文版)》2005,23(4):425-440
In this paper,we consider the cascadic multigrid method for the mortar P_1 noncon-forming element which is used to solve the Poisson equation and prove that the cascadicconjugate gradient method is accurate with optimal complexity. 相似文献
4.
1、引言 多重网格方法是求解偏微分方程的高效快速算法,在实际中得到广泛应用.[2][6]中考察了Morley元的多重网格方法,并用于双调和方程问题。 相似文献
5.
Zhongci Shi & Zhenghui Xie 《计算数学(英文版)》1998,16(5):385-394
1.IntroductionWeconsidersomemultigridalgorithmsforthebiharmonicequationdiscretizedbyMoneyelementonnonnestedmeshes.TOdefineamultigridalgorithm,certainintergridtransferoperatorhastobeconstructed.Throughtakingtheaveragesofthenodalvariables,weconstructanintergridtransferoperatorforMoneyelementonnonnestedmeshesthatsatisfiesacertainstableapproximationpropertywhichplaysakeyroleinmultigridmethodsfornonconformingplateelementsonnonnestedmeshes.Theso--calledregularity-approximaticnassurnptionisestablis… 相似文献
6.
抛物问题非协调元多重网格法 总被引:6,自引:0,他引:6
抛物问题非协调元多重网格法周叔子,文承标(湖南大学应用数学系)NONCONFORMINGELEMENTMULTIGRIDMETHODFORMRABOLICEQUATIONS¥ZhouShu-zi;WenCheng-biao(HunanUniversi... 相似文献
7.
1引 言
对于各向同性,均匀介质的平面线弹性问题,当Lamé常数λ→∞(泊松率v→0.5)时,即对于几乎不可压介质,通常的协调有限元格式的解往往不再收敛到原问题的解,或者达不到最优收敛阶,这就是所谓的闭锁现象(见[3],[7],[8]及[10]).究其原因,在通常的有限元分析中,其误差估计的系数与λ有关,当λ→∞时,该系数将趋于无穷大.因此为克服闭锁现象就需要构造特殊的有限元格式,使得当λ→∞时,有限元逼近解仍然收敛到原问题的解. 相似文献
8.
Cascadic multigrid technique for mortar Wilson finite element method of homogeneous boundary value planar linear elasticity is described and analyzed. First the mortar Wilson finite element method for planar linear elasticity will be analyzed, and the error estimate under L2 and H1 norm is optimal. Then a cascadic multigrid method for the mortar finite element discrete problem is described. Suitable grid transfer operator and smoother are developed which lead to an optimal cascadic multigrid method. Finally, the computational results are presented. 相似文献
9.
羊丹平 《高等学校计算数学学报(英文版)》1993,(2)
In this paper, we introduce two Schwarz type domain decomposition algorithms for solving boundary element equations, which decompose the original problem defined on global boundary surface into several ones defined on sub-domains so that they may be solved ileratively or parallelly. The convergence of these methods are also proved. 相似文献
10.
Abdellatif Agouzal 《计算数学(英文版)》2000,18(6):639-644
1. IlltroductionThe finite element approximation of the convection--diffusin equations has been investigated using several different approaches (see e.g. [3] [4] and the references therein).Previous analysis in primal formulation of these problems was done for two types ofapproximation schemes: one which produces a continuous piecewise polynomial approximation and one which produces a piecewise polynomial approximation which arecontinuous for certain number of moments accross interelement edge… 相似文献
11.
求解三维高次拉格朗日有限元方程的代数多重网格法 总被引:5,自引:0,他引:5
本文针对带有间断系数的三维椭圆问题,讨论任意四面体剖分下的二次拉格朗日有限元方程的代数多重网格法.通过分析线性和高次有限元空间之间的关系,我们给出了一种新的网格粗化算法和构造提升算子的代数途径.进一步,我们还对新的代数多重网格法给出了收敛性分析.数值实验表明这种代数多重网格法对求解二次拉格朗日有限元方程是健壮和有效的。 相似文献
12.
Ben-yu Guo 《计算数学(英文版)》2002,(1)
1. IntroductionSpectral method has been used successfu11y in computational fluid dynamics. FOr semi-periodic problems, we can use mixed FOurier-Chebyshev spectral method, FOurier spectral-finitedifference method and FOurier spectral-finite element method … 相似文献
13.
Hong-ying Man Zhong-ci Shi 《计算数学(英文版)》2006,24(1):59-80
In this paper,we discuss the finite volume element method of P_1-nonconforming quadri-lateral element for elliptic problems and obtain optimal error estimates for general quadri-lateral partition.An optimal eascadie multigrid algorithm is proposed to solve the non-symmetric large-scale system resulting from such discretization.Numerical experimentsare reported to support our theoretical results. 相似文献
14.
Huo-yuan Duan 《计算数学(英文版)》2002,20(1):57-64
1. IntroductionConsider the advection--diffusion equationin a bounded polygonal domain fl c IR2 with the boundary an, where o < K << 1 is thediffusion parameter, rr > 0 is a given positive constant, g(x) is a given vector field representingthe flow with V… 相似文献
15.
旋转Q1非协调元的V循环多重网格法 总被引:2,自引:0,他引:2
1.引言近年来,多重网格法已成为行之有效的偏微分方程数值解法,而对非协调元的多重网格法也有众多的研究,例在[1,3]中,作者研究了非协P1元的w循环多重网格法,[10]中,作者研究了*11s。n非协调元的V循环多重网格法.此外在K豆1,12]中,作者研究了板问题非协调有限元的多重网格法.最近,Rannacher和Turek同构造了所谓的QI非协调元,并用该元离散StokeS问题.而在问中,利用该元来计算晶体,数值效果非常好.同时在同中,作者给出了该元的误差估计和超收敛分析.最近,Chen和oswald同又讨论了该元的多重网格法,并证明了W循环… 相似文献
16.
17.
THE MORTAR ELEMENT METHOD FOR ROTATED Q1 ELEMENT 总被引:5,自引:0,他引:5
Jin-ru Chen 《计算数学(英文版)》2002,(3)
AbstractIn this paper, a mortar element version for rotated Q1 element is proposed. The optimal error estimate is proven for the rotated Q1 mortar element method. 相似文献
18.
In this paper, we study the mixed element method for Sobolev equations. A time-discretization procedure is presented and analysed and the optimal order error estimates are derived.For convenience in practical computation, an alternating-direction iterative scheme of the mixed fi-nite element method is formulated and its stability and converbence are proved for the linear prob-lem. A numerical example is provided at the end of this paper. 相似文献
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20.
This work develops a fully discrete implicit-explicit finite element scheme for a parabolic-ordinary system with a nonlinear reaction term which is known as the FitzHugh-Nagumo
model from physiology. The first-order backward Euler discretization for the time derivative, and an implicit-explicit discretization for the nonlinear reaction term are employed
for the model, with a simple linearization technique used to make the process of solving equations more efficient. The stability and convergence of the fully discrete implicit-explicit
finite element method are proved, which shows that the FitzHugh-Nagumo model is accurately solved and the trajectory of potential transmission is obtained. The numerical
results are also reported to verify the convergence results and the stability of the proposed
method. 相似文献