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971.
Jean M.‐S. Lubuma 《Numerical Methods for Partial Differential Equations》2008,24(3):699-727
The exterior Stokes problem between two parallel planes that are separated by a prismatic cylinder is extended to the interior of the prism by requiring the continuity of the velocity across the lateral faces. The well‐posedness of the exterior–interior problem is proved in suitable weighted Sobolev spaces. The solution is represented by Fourier series in the z‐variable. The Fourier coefficients, solutions of auxiliary two‐dimensional exterior–interior problems, are analyzed by viewing them as boundary integral equations of potential theory and global regularity of the densities, is established in weighted Sobolev spaces of traces. A boundary element method, with suitably refined mesh size, is implemented for the numerical treatment of the Fourier coefficients. This provides optimal convergent semi‐ and fully‐discrete spectral methods of Fourier–Galerkin type. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 相似文献
972.
Rakhim Aitbayev 《Numerical Methods for Partial Differential Equations》2008,24(2):518-534
A quadrature Galerkin scheme with the Bogner–Fox–Schmit element for a biharmonic problem on a rectangular polygon is analyzed for existence, uniqueness, and convergence of the discrete solution. It is known that a product Gaussian quadrature with at least three‐points is required to guarantee optimal order convergence in Sobolev norms. In this article, optimal order error estimates are proved for a scheme based on the product two‐point Gaussian quadrature by establishing a relation with an underdetermined orthogonal spline collocation scheme. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 相似文献
973.
Kamel Nafa 《国际流体数值方法杂志》2008,56(6):753-765
Two‐level low‐order finite element approximations are considered for the inhomogeneous Stokes equations. The elements introduced are attractive because of their simplicity and computational efficiency. In this paper, the stability of a Q1(h)–Q1(2h) approximation is analysed for general geometries. Using the macroelement technique, we prove the stability condition for both two‐ and three‐dimensional problems. As a result, optimal rates of convergence are found for the velocity and pressure approximations. Numerical results for three test problems are presented. We observe that for the computed examples, the accuracy of the two‐level bilinear approximation is compared favourably with some standard finite elements. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
974.
1 IntroductionConsider the functional differential equations (FDE's) with finite delay ofthe form:where x,(0) = x(t 0) for --r 5 0 5 0 with some r 2 0 and f: [T, co] x C RI with C = C([--r, 0], R') the space of continuous functions mapping [--r, 0]into l-dimensional real space RI. For any yi E C we define the norm of yi as:where l' I is any norm in RI.Inspired by the ideas in [l--3], we develop a new technique in this work tostudy the stability of FDE's, where the components xl) xZt… 相似文献
975.
The particle migration effects and fluid–particle interactions occurring in the flow of highly concentrated fluid–particle suspension in a spatially modulated channel have been investigated numerically using a finite volume method. The mathematical model is based on the momentum and continuity equations for the suspension flow and a constitutive equation accounting for the effects of shear‐induced particle migration in concentrated suspensions. The model couples a Newtonian stress/shear rate relationship with a shear‐induced migration model of the suspended particles in which the local effective viscosity is dependent on the local volume fraction of solids. The numerical procedure employs finite volume method and the formulation is based on diffuse‐flux model. Semi‐implicit method for pressure linked equations has been used to solve the resulting governing equations along with appropriate boundary conditions. The numerical results are validated with the analytical expressions for concentrated suspension flow in a plane channel. The results demonstrate strong particle migration towards the centre of the channel and an increasing blunting of velocity profiles with increase in initial particle concentration. In the case of a stenosed channel, the particle concentration is lowest at the site of maximum constriction, whereas a strong accumulation of particles is observed in the recirculation zone downstream of the stenosis. The numerical procedure applied to investigate the effects of concentrated suspension flow in a wavy passage shows that the solid particles migrate from regions of high shear rate to low shear rate with low velocities and this phenomenon is strongly influenced by Reynolds numbers and initial particle concentration. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
976.
Steen Markvorsen 《Geometriae Dedicata》2008,133(1):7-34
For a given combinatorial graph G a geometrization (G, g) of the graph is obtained by considering each edge of the graph as a 1-dimensional manifold with an associated metric g. In this paper we are concerned with minimal isometric immersions of geometrized graphs (G, g) into Riemannian manifolds (N
n
, h). Such immersions we call minimal webs. They admit a natural ‘geometric’ extension of the intrinsic combinatorial discrete Laplacian. The geometric Laplacian on
minimal webs enjoys standard properties such as the maximum principle and the divergence theorems, which are of instrumental
importance for the applications. We apply these properties to show that minimal webs in ambient Riemannian spaces share several
analytic and geometric properties with their smooth (minimal submanifold) counterparts in such spaces. In particular we use
appropriate versions of the divergence theorems together with the comparison techniques for distance functions in Riemannian
geometry and obtain bounds for the first Dirichlet eigenvalues, the exit times and the capacities as well as isoperimetric
type inequalities for so-called extrinsic R-webs of minimal webs in ambient Riemannian manifolds with bounded curvature.
相似文献
977.
Representations of distributive semilattices in ideal lattices of various algebraic structures 总被引:2,自引:0,他引:2
We study the relationships among existing results about representations of distributive semilattices by ideals in dimension
groups, von Neumann regular rings, C*-algebras, and complemented modular lattices. We prove additional representation results
which exhibit further connections with the scattered literature on these different topics.
Received March 2, 1998; accepted in final form November 9, 2000. 相似文献
978.
Summary In this contribution, the mechanical behaviour of different ZrO2/NiCr 80 20 compositions is analysed and compared with experimental findings. The microwave-sintered material is found to
possess a slightly dominant ceramic matrix for intermediate volume fractions. Its thermal expansion coefficient deviates from
the rule of mixture. The modulus and the stress strain behaviour can be simulated by a numerical homogenization procedure,
and the influence of residual stresses is found to be negligible. A newly introduced parameter (matricity) describes the mutual
circumvention of the phases and is found to strongly control the stress level of the composite, globally as well as locally.
Finally, a graded component and a metal/ceramic bi-material are compared for thermal as well as mechanical loading.
Received 23 November 1999; accepted for publication 26 May 2000 相似文献
979.
一种特殊设计约束面的有限元网格优化问题 总被引:3,自引:0,他引:3
网格设计质量的优劣是有限元分析的关键,对一些特殊的设计约束面,网格的优化设计是建模时需要首先研究解决的问题,本文对两种材料在几何尺寸差异很大情况下的有限元网格进行了优化设计并对其进行了讨论。 相似文献
980.
A high‐order element‐based Galerkin method is developed to solve the non‐divergent barotropic vorticity equation (BVE). The solution process involves solving a conservative transport equation for the vorticity fields and a Poisson equation for the stream function fields. The discontinuous Galerkin method is employed for solving the transport equation and a spectral element method (continuous Galerkin) is used for the Poisson equation. A third‐order strong stability preserving explicit Runge–Kutta scheme is used for time integration. A series of tests have been performed to validate the model, which include the evolution of an idealized tropical cyclone and interaction of dual vortices in close proximity. The numerical convergence study is performed by solving the BVE on the sphere where the analytic solution is known. The test results are consistent with physical observations, and the model exhibits exponential convergence. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献