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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
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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
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1. IntroductionBornemann and Deuflhaxd [2][3] have Presented a new take of multgiid methods,the sthcalled cascadic multigrid. Compared with usual multigrid ndhods, it reqno coarse grid correCtions at all that may be viewed as a "one way" multis. AnotherdiStinctive feature is performing more iterations on coarser levels so as to obtain leSSiterations on finer levels. Numerical openments show that this ndhod is yak effectivefor second order elliptic problems.In the paper3 we will consider the… 相似文献
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Sheng Zhang Dehao Yu 《计算数学(英文版)》2007,25(1):13-26
In this paper, some V-cycle multigrid algorithms are presented for the coupling system arising from the discretization of the Dirichlet exterior problem by coupling the natural boundary element method and finite element method. The convergence of these multigrid algorithms is obtained even with only one smoothing on all levels. The rate of convergence is found uniformly bounded independent of the number of levels and the mesh sizes of all levels, which indicates that these multigrid algorithms are optimal. Some numerical results are also reported. 相似文献
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芮洪兴 《数学物理学报(B辑英文版)》2004,24(1):129-138
Consider the finite volume element method for the thermal convection problem with the infinite Prandtl number. The author uses a conforming piecewise linear function on a fine triangulation for velocity and temperature, and a piecewise constant function on a coarse triangulation for pressure. For general triangulation the optimal order H^1 norm error estimates are given. 相似文献
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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
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Dai-quYang JenniferZhao 《计算数学(英文版)》2003,21(3):257-276
An iterative algorithm is proposed and analyzed based on a hybridized mized finite element method for numerically solving two-phase generalized Stefan interface problems with strongly discontinuous solutions,conormal derivatives,and coefficients.This algorithm iteratively solves small problems for each single phase with good accuracy and exchange information at the interface to advance the iteration until convergence ,following the idea of Schwarz Alternating Methods,Error estimates are derived to show that this algorithm always converges provided that relaxation parameters are suitably chosen,Numeric exper-iments with matching and non-matching grids at the interface from different phases are performed to show the accuracy of the method for capturing discontinuities in the solutions and coefficients.In contrast to standard numerical methods,the accuracy of our method does not seem to deteriorate as the coefficient discontinuity increases. 相似文献
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We consider an adaptive finite element method (AFEM) for obstacle problems associated with linear second order elliptic boundary value problems and prove a reduction in the energy norm of the discretization error which leads to R-linear convergence. This result is shown to hold up to a consistency error due to the extension of the discrete multipliers (point functionals) to H^-1 and a possible mismatch between the continuous and discrete coincidence and noncoincidence sets. The AFEM is based on a residual-type error estimator consisting of element and edge residuals. The a posteriori error analysis reveals that the significant difference to the unconstrained case lies in the fact that these residuals only have to be taken into account within the discrete noncoincidence set. The proof of the error reduction property uses the reliability and the discrete local efficiency of the estimator as well as a perturbed Galerkin orthogonality. Numerical results are given illustrating the performance of the AFEM. 相似文献
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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
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Huo-yuan Duan Qun Lin 《计算数学(英文版)》2006,24(2):157-168
This paper provides a proof for the uniform convergence rate (independently of the number of mesh levels) for the nonnested V-cycle multigrid method for nonsymmetric and indefinite second-order elliptic problems. 相似文献
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Yan-pingChen De-haoYu 《计算数学(英文版)》2003,21(6):825-832
In this paper the least-squares mixed finite element is considered for solving secondorder elliptic problems in two dimensional domains. The primary solution u and the flux er are approximated using finite element spaces consisting of piecewise polynomials of degree k and r respectively. Based on interpolation operators and an auxiliary projection,superconvergent H^1-error estimates of both the primary solution approximation uh and the flux approximation σh are obtained under the standard quasi-uniform assumption on finite element partition. The superconvergence indicates an accuracy of O(h^r 2) for the least-squares mixed finite element approximation if Raviart-Thomas or Brezzi-DouglasFortin-Marini elements of order r are employed with optimal error estimate of O(h^r l). 相似文献
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袁健华 《高等学校计算数学学报》2008,30(2):141-151
1引言设Ω∈R~2为Lipschitz单连通的有界闭区域,X为定义在Ω的Sobolev空间,a(·,·)和b(·,·)为X×X→C的有界双线性或半双线性泛函,考虑变分特征值问题:求(λ,u≠0)∈C×X使得a(u,v)=λb(u,u),(?)u∈X,其中a(·,·)满足X上的"V-强制性"条件或者连续的inf-sup条件,设M_h为Q区域上的正则三角形剖分,X_h∈X为定义在M_h有限元子空间,上述变分问题对应的有限元离散问题为:求(λ_h,u_h)∈R×X,u_h≠0使得 相似文献
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In this paper we extend the idea of interpolated coefficients for a semilinear problem to the triangular finite volume element method. We first introduce triangular finite volume element method with interpolated coefficients for a boundary value problem of semilinear elliptic equation. We then derive convergence estimate in Hi-norm, L2-norm and L∞-norm, respectively. Finally an example is given to illustrate the effectiveness of the proposed method. 相似文献
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Yanzhen Chang 《计算数学(英文版)》2012,30(6):629-642
In this paper, we propose adaptive finite element methods with error control for solving elasticity problems with discontinuous coefficients. The meshes in the methods do not need to fit the interfaces. We establish a residual-based a posteriori error estimate which is $λ$-independent multiplicative constants; the Lamé constant $λ$ steers the incompressibility. The error estimators are then implemented and tested with promising numerical results which will show the competitive behavior of the adaptive algorithm. 相似文献
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崔明 《高等学校计算数学学报》2002,24(3):206-211
1 引 言设Ω R2为具有光滑边界的有界区域,考虑非定常的,无量纲化的,而且带有热传导的粘性不可压缩流体力学问题:问题(Ⅰ):求u=(u1,u2),p,T满足: 相似文献