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A UNIFIED A POSTERIORI ERROR ANALYSIS FOR DISCONTINUOUS GALERKIN APPROXIMATIONS OF REACTIVE TRANSPORT EQUATIONS 总被引:5,自引:0,他引:5
Ji-ming Yang Yan-ping Chen 《计算数学(英文版)》2006,24(3):425-434
Four primal discontinuous Galerkin methods are applied to solve reactive transportproblems, namely, Oden-Babuska-Baumann DG (OBB-DG), non-symmetric interior penaltyGalerkin (NIPG), symmetric interior penalty Galerkin (SIPG), and incomplete interiorpenalty Galerkin (IIPG). A unified a posteriori residual-type error estimation is derivedexplicitly for these methods. From the computed solution and given data, explicit esti-mators can be computed efficiently and directly, which can be used as error indicators foradaptation. Unlike in the reference [10], we obtain the error estimators in L~2 (L~2) norm byusing duality techniques instead of in L~2 (H~1) norm. 相似文献
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采用改进的欧氏距离的检索算法解决区间特征属性的计算,并在此基础上解决案例模糊属性的相似度度量问题.采用PULL&PUSH调整策略,并主要采用GoodUpMatching(简称GUM)调整方法进行案例权重的调整.文章系统提出了一套案例检索及其权重优化方法.并以第三方电子集市的人力资源配置系统为实例,完成了该检索方法及权重优化方法的有效性和效率对比实验,验证了它的有效性及优化性. 相似文献
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本文研究了一类capillarity系统解的存在性问题.采用在乘积空间中定义非线性映射的方法,把capillarity系统转化为非线性算子方程.借助于Sobolev嵌入定理等技巧证明非线性映射具有紧性,进而利用非线性映射值域的性质得到非线性算子方程解的存在性的结论.并由此获得在一定条件下capillarity系统在L~(P1)(Ω)×L~(P2)(Ω)×…×L~(PM)(Ω)空间中存在非平凡解的结论,其中Ω为R~N(N≥1)中有界锥形区域且2N/N+1p_i+∞,i=1,2,…,M.本文所研究的问题和所采用的方法推广和补充了以往的相关研究工作. 相似文献
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传统的求解0-1规划问题方法大多属于直接离散的解法.现提出一个包含严格转换和近似逼近三个步骤的连续化解法:(1)借助阶跃函数把0-1离散变量转化为[0,1]区间上的连续变量;(2)对目标函数采用逼近折中阶跃函数近光滑打磨函数,约束条件采用线性打磨函数逼近折中阶跃函数,把0-1规划问题由离散问题转化为连续优化模型;(3)利用高阶光滑的解法求解优化模型.该方法打破了特定求解方法仅适用于特定类型0-1规划问题惯例,使求解0-1规划问题的方法更加一般化.在具体求解时,采用正弦型光滑打磨函数来逼近折中阶跃函数,计算效果很好. 相似文献
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基于市场需求是随机的,并且在进行市场销售前,就要确定每个阶段的生产数量的背景下,建立了具有规避风险的多阶段库存凸随机规划模型.该模型以最小化损失函数的期望值为目标函数,以规避风险为约束条件,以价值风险(VaR)和条件价值风险(CVaR)为风险度量;采用样本平均近似方法(SAA)求解该模型,并分析样本平均近似方法的收敛性;最后,给出数值结果. 相似文献
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Danxia Wang Yanan Li Hongen Jia 《Numerical Methods for Partial Differential Equations》2023,39(2):1251-1265
In this paper, we present a two-grid finite element method for the Allen-Cahn equation with the logarithmic potential. This method consists of two steps. In the first step, based on a fully implicit finite element method, the Allen-Cahn equation is solved on a coarse grid with mesh size H. In the second step, a linearized system whose nonlinear term is replaced by the value of the first step is solved on a fine grid with mesh size h. We give the energy stabilities of the traditional finite element method and the two-grid finite element method. The optimal convergence order of the two-grid finite element method in H1 norm is achieved when the mesh sizes satisfy h = O(H2). Numerical examples are given to demonstrate the validity of the proposed scheme. The results show that the two-grid method can save the CPU time while keeping the same convergence rate. 相似文献
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Chaobao Huang Martin Stynes 《Numerical Methods for Partial Differential Equations》2019,35(6):2076-2090
A time‐fractional reaction–diffusion initial‐boundary value problem with periodic boundary condition is considered on Q ? Ω × [0, T] , where Ω is the interval [0, l] . Typical solutions of such problem have a weak singularity at the initial time t = 0. The numerical method of the paper uses a direct discontinuous Galerkin (DDG) finite element method in space on a uniform mesh, with piecewise polynomials of degree k ≥ 2 . In the temporal direction we use the L1 approximation of the Caputo derivative on a suitably graded mesh. We prove that at each time level of the mesh, our L1‐DDG solution is superconvergent of order k + 2 in L2(Ω) to a particular projection of the exact solution. Moreover, the L1‐DDG solution achieves superconvergence of order (k + 2) in a discrete L2(Q) norm computed at the Lobatto points, and order (k + 1) superconvergence in a discrete H1(Q) seminorm at the Gauss points; numerical results show that these estimates are sharp. 相似文献
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We present an overlapping domain decomposition technique for solving the hypersingular integral equation on the sphere with
spherical splines. We prove that the condition number of the additive Schwarz operator is bounded by O(H/δ), where H is the size of the coarse mesh and δ is the overlap size, which is chosen to be proportional to the size of the fine mesh. In the case that the degree of the
splines is even, a better bound O(1 + log2(H/δ)) is proved. The method is illustrated by numerical experiments on different point sets including those taken from magsat satellite data. 相似文献
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Mohan K. Kadalbajoo Vikas Gupta Ashish Awasthi 《Journal of Computational and Applied Mathematics》2008,220(1-2):271-289
A numerical method is proposed for solving singularly perturbed one-dimensional parabolic convection–diffusion problems. The method comprises a standard implicit finite difference scheme to discretize in temporal direction on a uniform mesh by means of Rothe's method and B-spline collocation method in spatial direction on a piecewise uniform mesh of Shishkin type. The method is shown to be unconditionally stable and accurate of order O((Δx)2+Δt). An extensive amount of analysis has been carried out to prove the uniform convergence with respect to the singular perturbation parameter. Several numerical experiments have been carried out in support of the theoretical results. Comparisons of the numerical solutions are performed with an upwind finite difference scheme on a piecewise uniform mesh and exponentially fitted method on a uniform mesh to demonstrate the efficiency of the method. 相似文献
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C. I. Goldstein 《Numerische Mathematik》1982,38(1):61-82
Summary The finite element method with non-uniform mesh sizes is employed to approximately solve Helmholtz type equations in unbounded domains. The given problem on an unbounded domain is replaced by an approximate problem on a bounded domain with the radiation condition replaced by an approximate radiation boundary condition on the artificial boundary. This approximate problem is then solved using the finite element method with the mesh graded systematically in such a way that the element mesh sizes are increased as the distance from the origin increases. This results in a great reduction in the number of equations to be solved. It is proved that optimal error estimates hold inL
2,H
1 andL
, provided that certain relationships hold between the frequency, mesh size and outer radius. 相似文献
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A finite difference method for a time-dependent convection-diffusion problem in one space dimension is constructed using a Shishkin mesh. In two recent papers (Clavero et al. (2005) [2] and Mukherjee and Natesan (2009) [3]), this method has been shown to be convergent, uniformly in the small diffusion parameter, using somewhat elaborate analytical techniques and under a certain mesh restriction. In the present paper, a much simpler argument is used to prove a higher order of convergence (uniformly in the diffusion parameter) than in [2] and [3] and under a slightly less restrictive condition on the mesh. 相似文献
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A numerical study is made for solving a class of time-dependent singularly perturbed convection–diffusion problems with retarded terms which often arise in computational neuroscience. To approximate the retarded terms, a Taylor’s series expansion has been used and the resulting time-dependent singularly perturbed differential equation is approximated using parameter-uniform numerical methods comprised of a standard implicit finite difference scheme to discretize in the temporal direction on a uniform mesh by means of Rothe’s method and a B-spline collocation method in the spatial direction on a piecewise-uniform mesh of Shishkin type. The method is shown to be accurate of order O(M−1 + N−2 ln3N), where M and N are the number of mesh points used in the temporal direction and in the spatial direction respectively. An extensive amount of analysis has been carried out to prove the uniform convergence with respect to the singular perturbation parameter. Numerical results are given to illustrate the parameter-uniform convergence of the numerical approximations. Comparisons of the numerical solutions are performed with an upwind and midpoint upwind finite difference scheme on a piecewise-uniform mesh to demonstrate the efficiency of the method. 相似文献
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Guangzhi Du Qingtao Li Yuhong Zhang 《Numerical Methods for Partial Differential Equations》2020,36(6):1601-1610
In this paper, we consider the effect of adding a coarse mesh correction to the two-grid algorithm for the mixed Navier–Stokes/Darcy model. The method yields both L2 and H1 optimal velocity and piezometric head approximations and an L2 optimal pressure approximation. The method involves solving one small, coupled, nonlinear coarse mesh problem, two independent subproblems (linear Navier–Stokes equation and Darcy equation) on the fine mesh, and a correction problem on the coarse mesh. Theoretical analysis and numerical tests are done to indicate the significance of this method. 相似文献
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In this paper, a new adaptive nodes technique based on equi-distribution principles and dimension reduction is presented for irregular regions in three dimensional cases. The mesh generation is performed by first producing some adaptive nodes in a cube based on equi-distribution along the coordinate axes and then transforming the generated nodes to the physical domain followed by a refinement process. The mesh points produced are appropriate for meshless-type methods which need only some scattered points rather than a mesh with some smoothness properties. The effectiveness of the generated mesh points is examined by a collocation meshless method using a well known radial basis function, namely ?(r)?=?r 5 which is sufficiently smooth for our purpose. Some experimental results will be presented to illustrate the effectiveness of the proposed method. 相似文献
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Lin Mu Xiu Ye Shangyou Zhang 《Numerical Methods for Partial Differential Equations》2019,35(4):1497-1508
It is well known that convergence rate of finite element approximation is suboptimal in the L2 norm for solving biharmonic equations when P2 or Q2 element is used. The goal of this paper is to derive a weak Galerkin (WG) P2 element with the L2 optimal convergence rate by assuming the exact solution sufficiently smooth. In addition, our new WG finite element method can be applied to general mesh such as hybrid mesh, polygonal mesh or mesh with hanging node. The numerical experiments have been conducted on different meshes including hybrid meshes with mixed of pentagon and rectangle and mixed of hexagon and triangle. 相似文献