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1.
The quotient space of a K3 surface by a finite group is an Enriques surface or a rational surface if it is smooth. Finite groups where the quotient space are Enriques surfaces are known. In this paper, by analyzing effective divisors on smooth rational surfaces, the author will study finite groups which act faithfully on K3 surfaces such that the quotient space are smooth. In particular, he will completely determine effective divisors on Hirzebruch surfaces such that there is a finite Abelian co...  相似文献   

2.
We study spatially semidiscrete and fully discrete two-scale composite finite element method for approximations of the nonlinear parabolic equations with homogeneous Dirich-let boundary conditions in a convex polygonal domain in the plane.This new class of finite elements,which is called composite finite elements,was first introduced by Hackbusch and Sauter[Numer.Math.,75(1997),pp.447-472]for the approximation of partial differential equations on domains with complicated geometry.The aim of this paper is to introduce an efficient numerical method which gives a lower dimensional approach for solving par-tial differential equations by domain discretization method.The composite finite element method introduces two-scale grid for discretization of the domain,the coarse-scale and the fine-scale grid with the degrees of freedom lies on the coarse-scale grid only.While the fine-scale grid is used to resolve the Dirichlet boundary condition,the dimension of the finite element space depends only on the coarse-scale grid.As a consequence,the resulting linear system will have a fewer number of unknowns.A continuous,piecewise linear composite finite element space is employed for the space discretization whereas the time discretization is based on both the backward Euler and the Crank-Nicolson methods.We have derived the error estimates in the L∞(L2)-norm for both semidiscrete and fully discrete schemes.Moreover,numerical simulations show that the proposed method is an efficient method to provide a good approximate solution.  相似文献   

3.
In this paper we propose a method for improving the convergence rate of the mixed finite element approximations for the Stokes eigenvalue problem. It is based on a postprocessing strategy that consists of solving an additional Stokes source problem on an augmented mixed finite element space which can be constructed either by refining the mesh or by using the same mesh but increasing the order of the mixed finite element space. Dedicated to Ivan Hlaváček on the occasion of his 75th birthday  相似文献   

4.
A sparse grid stochastic collocation method combined with discontinuous Galerkin method is developed for solving convection dominated diffusion optimal control problem with random coefficients. By the optimal control theory, an optimality system is obtained for the problem, which consists of a state equation, a co-state equation and an inequality. Based on finite dimensional noise assumption of random field, the random coefficients are assumed to have finite term expansions depending on a finite number of mutually independent random variables in the probability space. An approximation scheme is established by using a discontinuous Galerkin method for the physical space and a sparse grid stochastic collocation method based on the Smolyak construction for the probability space, which leads to the solution of uncoupled deterministic problems. A priori error estimates are derived for the state, co-state and control variables. Numerical experiments are presented to illustrate the theoretical results.  相似文献   

5.
对二维定常的不可压缩的Navier-Stokes方程的局部和并行算法进行了研究.给出的算法是多重网格和区域分解相结合的算法,它是基于两个有限元空间:粗网格上的函数空间和子区域的细网格上的函数空间.局部算法是在粗网格上求一个非线性问题,然后在细网格上求一个线性问题,并舍掉内部边界附近的误差相对较大的解.最后,基于局部算法,通过有重叠的区域分解而构造了并行算法,并且做了算法的误差分析,得到了比标准有限元方法更好的误差估计,也对算法做了数值试验,数值结果通过比较验证了本算法的高效性和合理性.  相似文献   

6.
In the case of a finite number of subspaces in a given Hilbert space, by a theorem of J. von Neumann, the iteration of the product of projectors is always convergent. In a finite dimensional Hilbert space, this theorem has been generalized for affine subspaces. In this paper we construct an example which shows that this result does not hold in the infinite dimensional case.  相似文献   

7.
The measure-valued Fleming–Viot process is a diffusion which models the evolution of allele frequencies in a multi-type population. In the neutral setting the Kingman coalescent is known to generate the genealogies of the “individuals” in the population at a fixed time. The goal of the present paper is to replace this static point of view on the genealogies by an analysis of the evolution of genealogies. We encode the genealogy of the population as an (isometry class of an) ultra-metric space which is equipped with a probability measure. The space of ultra-metric measure spaces together with the Gromov-weak topology serves as state space for tree-valued processes. We use well-posed martingale problems to construct the tree-valued resampling dynamics of the evolving genealogies for both the finite population Moran model and the infinite population Fleming–Viot diffusion. We show that sufficient information about any ultra-metric measure space is contained in the distribution of the vector of subtree lengths obtained by sequentially sampled “individuals”. We give explicit formulas for the evolution of the Laplace transform of the distribution of finite subtrees under the tree-valued Fleming–Viot dynamics.  相似文献   

8.
It is proved that every value or semivalue on a linear symmetric subspace of finite games is the restriction to this subspace of a semivalue on the space of all finite games.The theorem is proved for the space of all finite games on a fixed finite set of players, and for the space of all games with a finite support on an infinite set of players (the universe of players).  相似文献   

9.
The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further research on the functional dimension, and obtain the following results: (1) They construct a countable Hilbert space, which is nuclear, but its functional dimension is infinite. (2) The functional dimension of a Banach space is finite if and only if this space is finite dimensional. (3) Let B be a Banach space, B* be its dual, and denote the weak * topology of B* by σ(B*,B). Then the functional dimension of (B*,σ(B*,B)) is 1. By the third result, a class of topological linear spaces with finite functional dimension is presented.  相似文献   

10.
Approximate Inertial Manifolds (AIMs) is approached by multilevel finite element method, which can be referred to as a Post-processed nonlinear Galerkin finite element method, and is applied to the model reduction for fluid dynamics, a typical kind of nonlinear continuous dynamic system from viewpoint of nonlinear dynamics. By this method, each unknown variable, namely, velocity and pressure, is divided into two components, that is the large eddy and small eddy components. The interaction between large eddy and small eddy components, which is negligible if standard Galerkin algorithm is used to approach the original governing equations, is considered essentially by AIMs, and consequently a coarse grid finite element space and a fine grid incremental finite element space are introduced to approach the two components. As an example, the flow field of incompressible flows around airfoil is simulated numerically and discussed, and velocity and pressure distributions of the flow field are obtained accurately. The results show that there exists less essential degrees-of-freedom which can dominate the dynamic behaviors of the discretized system in comparison with the traditional methods, and large computing time can be saved by this efficient method. In a sense, the small eddy component can be captured by AIMs with fewer grids, and an accurate result can also be obtained.  相似文献   

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