一类非线性发展方程的特征中心差分法

给出一类非线性发展方程的特征中心差分法,分别得到非规则网格上的位移u、速度u_t及其对空间变量x的一阶导数项的差分解和误差估计.所讨论方法的计算量与基于线性插值的特征差分法相当,其近似解与基于二次插值的特征差分法的近似解具有相同阶的误差估计,u,u_t对空间变量x的一阶导数近似均具有超收敛误差估计.数值试验说明了该方法的可行性和有效性.     

定常的磁流体动力学问题的Galerkin-Petrov最小二乘混合元方法

提出了定常的磁流体动力学方程的一种Galerkin-Petrov最小二乘混合元法,并导出Galerkin-Petrov最小二乘混合元解的存在性和误差估计．通过引入Galerkin-Petrov最小二乘混合有限元方法使得该方法的混合元空间之间的组合无需满足离散的Babuska-Brezzi稳定性条件,从而使得它们的混合有限元空间可以任意选取,并得到误差估计最优阶．     

基于Novozhilov理论连续弯箱位移参数的动态Bayes估计

推导了基于Novozhilov理论的简支弯箱有限曲条控制方程,并结合柔度法解决了连续弯箱的求解问题．建立了连续弯箱位移参数的动态Bayes误差函数,推导了相应的动态Bayes均值和方差表达式,提出步长的一维自动寻优方案后,结合共轭梯度法研究了连续弯箱位移参数的动态Bayes估计方法,同时给出了连续弯箱位移参数具体估计步骤．通过典型算例分析,总结了连续弯箱位移参数先验信息准确性判定方法及位移参数动态Bayes随机估计的其它重要结论．     

LONG TIME BEHAVIOR FOR SOLUTION OF INITIAL BOUNDARY VALUE PROBLEM OF ONE CLASS OF SYSTEMS WITH MULTIDIMENSIONAL INHOMOGENEOUS GBBM EQUATIONS

The following initial-boundary value problem for the systems with multidimensional inhomogeneous generalized Benjamin-Bona-Mahony ( GBBM ) equations is reviewed. The existence of global attractors of this problem was proved by means of a uniform priori estimate for time.     

一类多维非齐次GBBM方程初边值问题解的长时间行为

研究一类多维非齐次广义Benjamin-Bona-Mahony(GBBM)方程的初值边界问题,利用Sobolev插值不等式,做关于时间的一致性先验估计,证明该问题的整体吸引子的存在性．     

A TWO-LEVEL FINITE ELEMENT GALERKIN METHOD FOR THE NONSTATIONARY NAVIER-STOKES EQUATIONS I： SPATIAL DISCRETIZATION

In this article we consider a two-level finite element Galerkin method using mixed finite elements for the two-dimensional nonstationary incompressible Navier-Stokes equations. The method yields a $H^1$-optimal velocity approximation and a $L_2$-optimal pressure approximation. The two-level finite element Galerkin method involves solving one small, nonlinear Navier-Stokes problem on the coarse mesh with mesh size $H$, one linear Stokes problem on the fine mesh with mesh size $h << H$. The algorithm we study produces an approximate solution with the optimal, asymptotic in $h$, accuracy.     

A Summation Formula for Estimating the Surface Areas of Ellipsoids

In this paper a summation formula for finding the surface area of general ellipsoids is derived.     

CONVERGENCE OF AN ALTERNATING A-φ SCHEME FOR QUASI-MAGNETOSTATIC EDDY CURRENT PROBLEM

We propose in this paper an alternating A-$\phi$ method for the quasi-magnetostatic eddy current problem by means of finite element approximations. Bounds for continuous and discrete error in finite time are given. And it is verified that provided the time step $\tau$ is sufficiently small, the proposed algorithm yields for finite time $T$ an error of $O(h+\tau^{1/2})$ in the $L^2$-norm for the magnetic field $H(= \mu^{-1} \nabla \times A)$, where $h$ is the mesh size, $\mu$ the magnetic permeability.     

血液相容生医材料的合成研究15——苯乙烯型磺酸铵内盐单体的合成及其聚合物的抗血小板粘附性能

两性离子不凝血生物材料;血液相容生医材料的合成研究15——苯乙烯型磺酸铵内盐单体的合成及其聚合物的抗血小板粘附性能     

三阶奇摄动非线性边值问题

利用微分不等式理论,研究了某一类三阶奇摄动非线性边值问题。以二阶边值问题的已知结果为基础,引入Volterra型积分算子,建立了三阶非线性边值问题的上下解方法。在适当条件下,构造出具体的上下解,得出解的存在性和渐进估计。结果表明这种技巧也为三阶奇摄动边值问题的研究提出了崭新的思路。最后举例验证文中定理的正确性。