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We propose and analyze a C^0 spectral element method for a model eigenvalue problem with discontinuous coefficients in the one dimensional setting. A super-geometric rate of convergence is proved for the piecewise constant coefficients case and verified by numerical tests. Furthermore, the asymptotical equivalence between a Gauss-Lobatto collocation method and a spectral Galerkin method is established for a simplified model. 相似文献
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本文讨论了一类半线性抛物型积分微分方程的间断时空有限元方法.利用有限元和有限差分方法相结合的技巧,在时间离散区间内,利用Radau点处Lagrange插值多项式的特性,去掉间断时空有限元的传统证明过程中对时空网格的限制条件,并给出了时间最大模、空间L_2模,即L_∞(L_2)模的误差估计. 相似文献
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Lung-an Ying 《计算数学(英文版)》2000,18(6):657-672
1. IntroductionThe infinite element method has been successfully applied to some boundary valueproblems of partial differential equations, where the solutions possess corner singularpoints or the domains are exterior ones. If the equations are invariant under similaritytransformation the approaches have been given in [11] [131 for singular solutions, and in[12][15][181119] for the exterior problems. If the equations do not admit the above invariant property? one approach has been given in [14]… 相似文献
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In this paper, we consider the finite element method and discontinuous Galerkin method for the stochastic Helmholtz equation in R^d (d = 2, 3). Convergence analysis and error estimates are presented for the numerical solutions. The effects of the noises on the accuracy of the approximations are illustrated. Numerical experiments are carried out to verify our theoretical results. 相似文献
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构造具有广义边界条件的四阶线性抛物型方程的混合间断时空有限元格式,利用混合有限元方法将高阶方程降阶,利用空间连续而时间允许间断的时空有限元方法离散方程,证明了离散解的存在唯一性,稳定性和收敛性,并给出数值算例验证了方法的有效性. 相似文献
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Dao-qi Yang 《计算数学(英文版)》1998,16(2):141-151
1.IntroductionNolloverlappillgdomaindecolllpositionnletllodshavereceivedalotofattentionlenlsilllldallowefficielltparallelisnl.F'Orarecentdevelopmelltofthesemethods,werefertot… 相似文献
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Dong-ying Hua Lie-heng Wang 《计算数学(英文版)》2005,23(4):441-448
Based on the analysis of [7] and [10], we present the mixed finite element approximation of the variational inequality resulting from the contact problem in elasticity. The convergence rate of the stress and displacement field are both improved from O(h3/4) to quasi-optimal O(h│logh│^1/4). If stronger but reasonable regularity is available, the convergence rate can be optimal O(h). 相似文献
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王海明 《高校应用数学学报(A辑)》1997,(3):361-368
讨论部分机器个已安排有工件的情况下的P∥Cmax问题,证明了Multifit算法的最差情况指标满足Rm(MF「k)」∈(1.23,1.275+1/2^k),m≥4。 相似文献
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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
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Houde Han Zhongyi Huang 《计算数学(英文版)》2008,26(5):728-739
In this paper, we propose a tailored-finite-point method for the numerical simulation of the Helmholtz equation with high wave numbers in heterogeneous medium. Our finite point method has been tailored to some particular properties of the problem, which allows us to obtain approximate solutions with the same behaviors as that of the exact solution very naturally. Especially, when the coefficients are piecewise constant, we can get the exact solution with only one point in each subdomain. Our finite-point method has uniformly convergent rate with respect to wave number k in L^2-norm. 相似文献
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In this paper,Chebyshev pseudospectral-finite element schemes are proposed for solving three dimensional vorticity equation.Some approximation results in nonisotropic Sobolev spaces are given.The generalized stability and the convergence are proved strictly.The numerical results show the advantages of this method.The technique in this paper is also applicable to other three-dimensional nonlinear problems in fluid dynamics. 相似文献
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Yinnian He Jinchao Xu Aihui Zhou 《计算数学(英文版)》2006,24(3):227-238
Based on two-grid discretizations, in this paper, some new local and parallel finiteelement algorithms are proposed and analyzed for the stationary incompressible Navier-Stokes problem. These algorithms are motivated by the observation that for a solutionto the Navier-Stokes problem, low frequency components can be approximated well by arelatively coarse grid and high frequency components can be computed on a fine grid bysome local and parallel procedure. One major technical tool for the analysis is some locala priori error estimates that are also obtained in this paper for the finite element solutionson general shape-regular grids. 相似文献