共查询到16条相似文献,搜索用时 93 毫秒
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本文研究了一类椭圆型奇异摄动问题.利用Bakhvalov-Shishkin网格上的差分方法,获得了数值解一致一阶收敛于真解的结果. 相似文献
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采用非对称内罚间断有限元方法(以下简称NIPG方法)求解一维对流扩散型奇异摄动问题.理论上证明了采用拉格朗日线性元的NIPG方法在Bakhvalov-Shishkin网格上具有最优阶的一致收敛性,即在能量范数度量下其误差估计为O(N~(-1)),其中N为网格剖分中单元个数.数值算例验证了理论分析的正确性. 相似文献
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该文在Bakhvalov-Shishkin网格上求解具有左边界层或右边界层的对流扩散方程,并采用差分进化算法对Bakhvalov-Shishkin网格中的参数进行优化,获得了该网格上具有最优精度的数值解.对三个算例进行了数值模拟,数值结果表明:采用差分进化算法求解具有较高的计算精度和收敛性,特别是边界层的数值解精度明显... 相似文献
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在Shishkin格上分析了高阶SIPG方法求解一维对流扩散型奇异摄动问题的一致收敛性.取k(k≥1)次分片多项式和网格剖分单元数为民时,在能量范数度量下Shishkin网格上可获得■((N~(-1)lnN)~k)的一致误差估计.在数值算例部分对理论分析结果进行了验证. 相似文献
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刘春辉 《高校应用数学学报(A辑)》2019,34(2)
拓扑结构是逻辑代数研究领域的重要研究内容之一,为了揭示否定非对合剩余格上的拓扑结构,基于正规模糊理想诱导的同余关系在否定非对合剩余格上构造一致拓扑空间并讨论其拓扑性质.证明了:(1)一致拓扑空间是第一可数,零维,非连通,局部紧的完全正则空间;(2)一致拓扑空间是T_1空间当且仅当是T_2空间;(3)否定非对合剩余格中格运算和伴随运算关于一致拓扑都是连续的,从而构成拓扑否定非对合剩余格.同时,获得了一致拓扑空间是紧空间和离散空间的充分必要条件.最后,讨论了拓扑否定非对合剩余格中代数同构与拓扑同胚间的关系.对从拓扑层面进一步揭示否定非对合剩余格的内部特征具有一定的促进作用. 相似文献
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将一致小于关系移植到一般偏序集上,同时引入了上界小于关系,定义了偏序集的一致连续性和上界连续性.给出了一致连续偏序集的等价刻画,探讨了一致连续偏序集所具有的性质.主要结果有:(1)证明了偏序集上的一致连续性,上界连续性与s-超连续性均等价;(2)在交半格条件下,偏序集的一致连续性等价于它的每一主理想一致连续;(3)在并半格条件下,偏序集的一致连续性蕴含连续性,反之不成立;(4)一致完备的一致连续偏序集均是连续bc-dcpo,且每个主理想均为完全分配格;(5)在一致完备的条件下,一致连续性对主滤子,对闭区间,对Scott S-集以及对一致连续投射像均是可遗传的.文中也构造了若干实用的反例. 相似文献
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本文为一类带有移动界面的守恒律方程提出了耦合高分辨率格式的数值算法.这种算法是在一致大小的笛卡尔网格上导出而满足标准的双曲型稳定条件.文末列举数值算例研究这种算法的收敛性和数值精度. 相似文献
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四阶奇异摄动边值问题在自适应网格上的一致收敛分析 总被引:1,自引:0,他引:1
we study a difference scheme for the fourth-order singular pertur-bation differential equation on the Bakhvalov-Shishkin grid by Green‘‘s function.The method is shown to be uniformly convergent with respect to the perturbation parameter,of order N^-2 in the maxmum norm on Bakhvalov-Shishkin meshes.Numerical results support our theoretical results. 相似文献
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Defect correction method is used for two parameter singular perturbation problem on Bakhvalov-Shishkin mesh. Use of defect correction method on Bakhvalov-Shishkin mesh gives a second order convergence. A posteriori error estimate is obtained. The numerical examples are given to establish the second order convergence in practice. 相似文献
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We explore the geometry of isothermic meshes, conical meshes, and asymptotic meshes around the Christoffel dual construction
of a discrete minimal surface. We present a discrete Legendre transform which realizes discrete minimal surfaces as conical
meshes. Conical meshes turn out to be infinitesimally flexible if and only if their spherical image is isothermic, which implies
that discrete minimal surfaces constructed in this way are infinitesimally flexible, and therefore possess reciprocal-parallel
meshes. These are discrete minimal surfaces in their own right. In our study of relative kinematics of infinitesimally flexible
meshes, we encounter characterizations of flexibility and isothermicity which are of incidence-geometric nature and are related
to the classical Desargues configuration. The Lelieuvre formula for asymptotic meshes leads to another characterization of
isothermic meshes in the sphere which is based on triangle areas. 相似文献
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Error analysis of staggered finite difference finite volume schemes on unstructured meshes
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Qingshan Chen 《Numerical Methods for Partial Differential Equations》2017,33(4):1159-1182
This work combines the consistency in lower‐order differential operators with external approximations of functional spaces to obtain error estimates for finite difference finite volume schemes on unstructured nonuniform meshes. This combined approach is first applied to a one‐dimensional elliptic boundary value problem on nonuniform meshes, and a first‐order convergence rate is obtained, which agrees with the results previously reported. The approach is also applied to the staggered Marker‐and‐Cell scheme for the two‐dimensional incompressible Stokes problem on unstructured meshes. A first‐order convergence rate is obtained, which improves over a previously reported result in that it also holds on unstructured meshes. For both problems considered in this work, the convergence rate is one order higher on meshes satisfying special requirements. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1159–1182, 2017 相似文献
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We explore the geometry of isothermic meshes, conical meshes, and asymptotic meshes around the Christoffel dual construction
of a discrete minimal surface. We present a discrete Legendre transform which realizes discrete minimal surfaces as conical
meshes. Conical meshes turn out to be infinitesimally flexible if and only if their spherical image is isothermic, which implies
that discrete minimal surfaces constructed in this way are infinitesimally flexible, and therefore possess reciprocal-parallel
meshes. These are discrete minimal surfaces in their own right. In our study of relative kinematics of infinitesimally flexible
meshes, we encounter characterizations of flexibility and isothermicity which are of incidence-geometric nature and are related
to the classical Desargues configuration. The Lelieuvre formula for asymptotic meshes leads to another characterization of
isothermic meshes in the sphere which is based on triangle areas.
Authors’ addresses: Johannes Wallner (corresponding author), Institut für Geometrie, TU Graz, Kopernikusgasse 24, A 8010 Graz,
Austria; Helmut Pottmann, Institut für Diskrete Mathematik und Geometrie, TU Wien, Wiedner Hauptstr. 8-10/104, A 1040 Wien,
Austria 相似文献
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Based on polyhedral splines, some multivariate splines of different orders
with given supports over arbitrary topological meshes are developed. Schemes for
choosing suitable families of multivariate splines based on pre-given meshes are
discussed. Those multivariate splines with inner knots and boundary knots from
the related meshes are used to generate rational spline shapes with related control
points. Steps for up to $C^2$-surfaces over the meshes are designed. The relationship
among the meshes and their knots, the splines and control points is analyzed. To
avoid any unexpected discontinuities and get higher smoothness, a heart-repairing
technique to adjust inner knots in the multivariate splines is designed.With the theory above, bivariate $C^1$-quadratic splines over rectangular meshes are
developed. Those bivariate splines are used to generate rational $C^1$-quadratic surfaces over the meshes with related control points and weights. The properties of
the surfaces are analyzed. The boundary curves and the corner points and tangent
planes, and smooth connecting conditions of different patches are presented. The $C^1$−continuous connection schemes between two patches of the surfaces are presented. 相似文献