广义神经传播方程的低阶H~1-Galerkin混合元方法

讨论了广义神经传播方程的低阶H~1-Galerkin混合元方法.其逼近空间不需要满足LBB条件,并且在不需要采用Ritz投影的情况下,通过插值算子,平均值技巧和高精度分析结果得到了超逼近性质,进而通过插值后处理技术导出了H~1-模的整体超收敛结果.     

拟线性粘弹性方程混合有限元分析

主要讨论拟线性粘弹性方程的Bernadi-Raugel混合有限元方法,给出了逼近解和精确解的收敛性分析.同时,基于积分恒等式技巧导出了超逼近性质,并进一步利用插值后处理技术得到了整体超收敛结果.     

Stokes问题非协调混合有限元超收敛分析

本文通过引入全新的技巧,研究了Stokes问题的非协调混合有限元方法,得到了关于速度与压力的超逼近性质.进一步地通过构造一个恰当的插值后处理算子,还得到了关于速度的整体超收敛结果.     

粘弹性方程混合有限元超收敛分析

运用Bernadi-Raugel混合元对粘弹性方程进行了有限元分析,基于积分恒等式技巧得到了相应的超逼近性质,并进一步利用插值后处理技术给出了整体超收敛结果.     

拟线性双相滞热传导方程的双线性元高精度分析及外推

研究一类拟线性双相滞热传导方程的双线性有限元逼近,利用该元的Ritz投影和插值相结合的技巧,并结合高精度分析和插值后处理技术分别导出了半离散和全离散格式的超逼近和超收敛结果.同时通过构造合适的辅助问题,对半离散格式导出了具有三阶精度的外推解.     

非线性Sobolev-Galpern型湿气迁移方程的非协调类Carey元超收敛分析

主要目的是将非协调类Carey元应用于非线性Sobolev-Galpern型湿气迁移方程.借助于单元的特殊性质(即在能量模意义下相容误差比插值误差高一阶)、线性三角元的高精度分析以及平均值技巧,得到了解的超逼近性质.进一步地利用插值后处理技术导出了整体超收敛结果.     

带有阻尼项的非线性抛物积分微分方程的非协调混合有限元方法

研究带有阻尼项的非线性抛物积分微分方程的非协调混合有限元(EQ_1~(rot)+Q_(10)×Q_(01))方法,直接利用单元插值的性质,运用高精度分析和导数转移技巧,导出了半离散格式的超逼近性质,同时利用插值后处理技术,导出了相应的O(h~2)阶整体超收敛结果,并通过构造一个合适的外推格式得到了O(h~3)阶的外推解.     

粘弹性方程ACM有限元的超收敛分析和外推

本文通过积分恒等式技巧和插值后处理技术,得到了粘弹性方程ACM有限元的超逼近和超收敛性质.进一步利用Bramble-Hilbert引理构造了一个合适的外推格式,得到了比以往文献高一阶的外推结果.     

非线性伪双曲积分微分方程的类Carey元超收敛分析

将非协调三角形类Carey元应用于非线性伪双曲积分微分方程进行了超收敛分析.利用该元在能量模意义下非协调误差比插值误差高一阶的特殊性质,线性三角形元的高精度分析结果及平均值技巧,在抛弃传统的Ritz-Volterra投影的情形下,得到了半离散格式能量模意义下的超逼近性质.进一步地,借助插值后处理技术,导出了相应的整体超收敛结果.     

半线性抛物方程各向异性最低阶R-T混合元超收敛分析

利用各向异性判别定理验证了最低阶数R-T混合元具有各向异性特征.利用积分恒等式技巧,得到了R-T元对半线性抛物方程的超逼近性质.通过构造新的插值后处理格式,导出了超收敛结果及后验误差估计.     

带弱奇异核非线性积分微分方程的有限元分析

讨论了带弱奇异核的非线性抛物积分微分方程的Hermite型各向异性矩形元逼近.在各向异性网格下导出了关于Riesz投影的L~2和H~1模的误差估计.在半离散和向后欧拉全离散格式下,基于Riesz投影的性质并利用平均值技巧,分别得到了L~2模意义下的最优误差估计.     

DECAY OF ENERGY FOR A DISSIPATIVE ANISOTROPIC ELASTIC SYSTEM

In this article, we study the large-time behavior of energy for a N-dimensional dissipative anisotropic elastic system. By means of multiplicative techniques, energy method, and Zuazua’s estimate technique, we prove the decay property of energy for anisotropic elastic system.     

二阶椭圆问题新混合元模型的超收敛分析及外推

对二阶椭圆问题通过＂增补＂办法导出一个新的混合模型.在各向异性网格下,利用积分恒等式技巧得到了真解与ECHL元近似解的超逼近性质.同时基于插值后处理技术导出了整体超收敛.进一步,通过渐进误差展开和分裂外推,得到了比通常的误差估计更高一阶的收敛速度.     

The spline collocation method for parabolic boundary integral equations on smooth curves

Summary. We consider the spline collocation method for a class of parabolic pseudodifferential operators. We show optimal order convergence results in a large scale of anisotropic Sobolev spaces. The results cover the classical boundary integral equations for the heat equation in the general case where the spatial domain has a smooth boundary in the plane. Our proof is based on a localization technique for which we use our recent results proved for parabolic pseudodifferential operators. For the localization we need also some special spline approximation results in anisotropic Sobolev spaces. Received May 17, 2001 / Revised version received February 19, 2002 / Published online April 17, 2002     

Nonlinear buckling and postbuckling of a shear-deformable anisotropic laminated cylindrical panel under axial compression

The nonlinear buckling and postbuckling of a shear-deformable anisotropic laminated cylindrical panel of finite length is investigated based on a boundary-layer theory for buckling. The layers of the panel are assumed to be linearly elastic. The governing equations are based on Reddy’s higher-order shear deformation theory of shells and include the von Karman-type kinematic nonlinearity and extension/twist, extension/flexure, and flexure/twist couplings. The nonlinear prebuckling deformations and the initial geometric imperfections of the panel are both taken into account. The postbuckling behavior of the panel under axial compression is analyzed. A singular perturbation technique is employed to determine its buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect moderately thick anisotropic laminated cylindrical panels with different geometric parameters and stacking sequences. The new finding reveals that there arises a compressive stress along with an associate shear stress and twisting when a moderately thick anisotropic laminated cylindrical panel is subjected to axial compression.     

Polynomial preserving recovery for quadratic elements on anisotropic meshes

Polynomial preserving gradient recovery technique under anisotropic meshes is further studied for quadratic elements. The analysis is performed for highly anisotropic meshes where the aspect ratios of element sides are unbounded. When the mesh is adapted to the solution that has significant changes in one direction but very little, if any, in another direction, the recovered gradient can be superconvergent. The results further explain why recovery type error estimator is robust even under nonstandard and highly distorted meshes. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Scattering on an anisotropic potential in a constant electric field

The scattering of a particle on an anisotropic potential in a constant electric field is considered. Conditions on the anisotropic decay of the potential that insure asymptotic completeness without modifications of the wave operators are obtained. The paper uses the mixed approach wherein the Enss method is applied to one part of the variables, whereas the other part is treated using the smoothness technique. Bibliography: 12 titles. Translated fromZapiski Naucnykh Seminarov POMI, Vol. 230, 1995, pp. 203–214. Translated by A. B. Pushnitskii.     

New anisotropic models from isotropic solutions

We establish an algorithm that produces a new solution to the Einstein field equations, with an anisotropic matter distribution, from a given seed isotropic solution. The new solution is expressed in terms of integrals of known functions, and the integration can be completed in principle. The applicability of this technique is demonstrated by generating anisotropic isothermal spheres and anisotropic constant density Schwarzschild spheres. Both of these solutions are expressed in closed form in terms of elementary functions, and this facilitates physical analysis. Copyright © 2005 John Wiley & Sons, Ltd.     

抛物问题各向异性有限元的超收敛分析

本文研究具有各向异性特征的双二次元对二阶抛物方程的逼近.通过积分恒等式和插值后处理技术,在各向异性网格下得到了相应的超逼近和超收敛结果.