共查询到20条相似文献,搜索用时 15 毫秒
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In this paper, we are concerned with uniform superconvergence of Galerkin methods for singularly perturbed reaction-diffusion problems by using two Shishkin-type meshes. Based on an estimate of the error between spline interpolation of the exact solution and its numerical approximation, an interpolation post-processing technique is applied to the original numerical solution. This results in approximation exhibit superconvergence which is uniform in the weighted energy norm. Numerical examples are presented to demonstrate the effectiveness of the interpolation post-processing technique and to verify the theoretical results obtained in this paper. 相似文献
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Ziqing Xie Zhimin Zhang 《计算数学(英文版)》2007,25(2):185-200
The convergence and superconvergence properties of the discontinuous Galerkin (DG) method for a singularly perturbed model problem in one-dimensional setting are studied. By applying the DG method with appropriately chosen numerical traces, the existence and uniqueness of the DG solution, the optimal order L2 error bounds, and 2p+ 1-order superconvergence of the numerical traces are established. The numerical results indicate that the DG method does not produce any oscillation even under the uniform mesh. Numerical experiments demonstrate that, under the uniform mesh, it seems impossible to obtain the uniform superconvergence of the numerical traces. Nevertheless, thanks to the implementation of the so-called Shishkin-type mesh, the uniform 2p + 1-order superconvergence is observed numerically. 相似文献
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A numerical method based on finite difference method with variable mesh is given for self-adjoint singularly perturbed two-point boundary value problems. To obtain parameter- uniform convergence, a variable mesh is constructed, which is dense in the boundary layer region and coarse in the outer region. The uniform convergence analysis of the method is discussed. The original problem is reduced to its normal form and the reduced problem is solved by finite difference method taking variable mesh. To support the efficiency of the method, several numerical examples have been considered. 相似文献
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In the present paper the edge stabilization technique is applied to a convection-diffusion problem with exponential boundary layers on the unit square, using a Shishkin mesh with bilinear finite elements in the layer regions and linear elements on the coarse part of the mesh. An error bound is proved for ‖πu-u^h‖Е, where πu is some interpolant of the solution u and uh the discrete solution. This supercloseness result implies an optimal error estimate with respect to the L2 norm and opens the door to the application of postprocessing for improving the discrete solution. 相似文献
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本文考虑如下一类具转向点椭圆型方程奇异摄动问题的数值解法文[1]已经研究了该问题的渐近解.本文在得到渐近解余项的更好估计式后,证明了所构造的差分格式关于小参数ε的一致收敛结果.误差估计达到α阶,其中. 相似文献
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This paper presents and analyzes a monotone domain decomposition algorithm for solving nonlinear singularly perturbed reaction-diffusion problems of parabolic type. To solve the nonlinear weighted average finite difference scheme for the partial differential equation, we construct a monotone domain decomposition algorithm based on a Schwarz alternating method and a box-domain decomposition. This algorithm needs only to solve linear discrete systems at each iterative step and converges monotonically to the exact solution of the nonlinear discrete problem. domain decomposition algorithm is estimated The rate of convergence of the monotone Numerical experiments are presented. 相似文献
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1991MRSubjectClassification35B2535K57Theauthorsstudiedakilldofsingularlypertllrbedproblemsin[1]-[61.Nowwe't()llsiderthefollowingsingularlyperturbedproblemforthenonlocalboulldaryconditionsouteof~Li'Ui=.fi(X,.UljUZj'',JINN,~),0相似文献
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解二阶奇异摄动两点边界值问题的差分方法 总被引:2,自引:0,他引:2
In this paper,a difference scheme in a special mesh is presented for solving the singluarly perturbed two-point boundayr value problems,.It is shown that the convergence order is O(N^-2)uniformly with respect to the perturbation parameter ε.The numerical examples are given underline the theoretical results. 相似文献
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Zhi-min Zhang 《计算数学(英文版)》2002,(6)
In this work, a singularly perturbed two-point boundary value problem of convection-diffusion type is considered. An hp version finite element method on a strongly graded piecewise uniform mesh of Shishkin type is used to solve the model problem. With the analytic assumption of the input data, it is shown that the method converges exponentially and the convergence is uniformly valid with respect to the singular perturbation parameter. 相似文献
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The purpose of this work is to implement a discontinuous Galerkin(DG) method with a one-sided flux for a singularly perturbed Volterra integro-differential equation(VIDE)with a smooth kernel.First,the regularity property and a decomposition of the exact solution of the singularly perturbed VIDE with the initial condition are provided.Then the existence and uniqueness of the DG solution are proven.Then some appropriate projection-type interpolation operators and their corresponding approximation ... 相似文献
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迭代极小残差方法是求解大型线性方程组的常用方法, 通常用残差范数控制迭代过程.但对于不适定问题, 即使残差范数下降, 误差范数未必下降. 对大型离散不适定问题,组合广义最小误差(GMERR)方法和截断奇异值分解(TSVD)正则化方法, 并利用广义交叉校验准则(GCV)确定正则化参数,提出了求解大型不适定问题的正则化GMERR方法.数值结果表明, 正则化GMERR方法优于正则化GMRES方法. 相似文献
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唐荣荣 《Annals of Differential Equations》2004,20(3):278-282
In this paper, a class of strongly nonlinear singularly perturbed interior layer problems are considered by the theory of differential inequalities and the corrective theory of interior layer. The existence of solution is proved and the asymptotic behavior of solution for the boundary value problems are studied. And the satisfying result is obtained. 相似文献
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Jian-lin Jiang Bo Chen 《计算数学(英文版)》2006,24(4):527-538
This paper investigates various Weber problems including unconstrained Weber problems and constrained Weber problems under l1, l2 and l∞-norms. First with a transformation technique various Weber problems are turned into a class of monotone linear variational inequalities. By exploiting the favorable structure of these variational inequalities, we present a new projection-type method for them. Compared with some other projection-type methods which can solve monotone linear variational inequality, this new projection-type method is simple in numerical implementations and more efficient for solving this class of problems; Compared with some popular methods for solving unconstrained Weber problem and constrained Weber problem, a singularity would not happen in this new method and it is more reliable by using this new method to solve various Weber problems. 相似文献
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Qi-nian Jin 《计算数学(英文版)》1999,(3)
1.IntroductionInthispaperweconsiderthenonlinearproblemsoftheformF(x)=co,(1)whereF:D(F)CX-- YisanonlinearoperatorbetweenrealHilbertspacesXandYandcoER(F).ThenormsinXandYwillbedenotedby11'IIxand11'flyrespectively.Wearemainlyinterestedinthoseproblemsofth... 相似文献