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一般椭圆型方程双线性有限元解误差展开
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作者 罗平 《怀化学院学报》 1992年第5期58-63,共6页
本文以简单明了的方法给出一般椭圆型方程双线性元的误差展开式。
关键词 双线性元 非均匀矩形剖分 渐近误差展开
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Stokes方程组Hood-Taylor元的分裂外推 被引量:2
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作者 林甲富 雷俊丽 《北京理工大学学报》 EI CAS CSCD 北大核心 2004年第11期1020-1023,1029,共5页
考虑拟一致矩形网格上Stokes方程组Hood-Taylor元的多参数渐近误差展开和分裂外推。在每个单元上用Bramble-Hilbert引理确定微分方程精确解与有限元插值之间积分式的主项。由连续性条件相邻两个单元上其主项的某些部分可以相互抵消,经... 考虑拟一致矩形网格上Stokes方程组Hood-Taylor元的多参数渐近误差展开和分裂外推。在每个单元上用Bramble-Hilbert引理确定微分方程精确解与有限元插值之间积分式的主项。由连续性条件相邻两个单元上其主项的某些部分可以相互抵消,经求和后,得到整个求解区域上的主项。对该主项引入辅助问题并利用Stokes问题解的正则性理论给出精确解与有限元插值间的一个误差渐近展开式。有限元解经插值后处理和分裂外推后,与通常的误差估计相比,收敛速度提高了一阶。 展开更多
关键词 Stokes方程组 Hood-Taylor元 分裂外推 多参数渐近误差展开
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奇异两点边值问题改进的梯形公式外推方法
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作者 唐永超 王同科 《天津师范大学学报(自然科学版)》 CAS 2015年第4期5-7,19,共4页
研究奇异两点边值问题的高精度数值方法.首先,将奇异两点边值问题转化为奇异积分的计算问题.其次,利用改进的复合梯形公式离散奇异积分,针对几种不同情形给出了误差渐近展开式.再次,由误差估计式设计了一种改进的龙贝格算法,利用该算法... 研究奇异两点边值问题的高精度数值方法.首先,将奇异两点边值问题转化为奇异积分的计算问题.其次,利用改进的复合梯形公式离散奇异积分,针对几种不同情形给出了误差渐近展开式.再次,由误差估计式设计了一种改进的龙贝格算法,利用该算法可以得到问题的高精度数值解.最后,通过数值算例说明了算法的有效性. 展开更多
关键词 奇异两点边值问题 复合梯形积分公式 分数阶泰勒展开 误差展开 龙贝格算法
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Extrapolation methods to compute hypersingular integral in boundary element methods 被引量:6
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作者 LI Jin ZHANG XiaoPing YU DeHao 《Science China Mathematics》 SCIE 2013年第8期1647-1660,共14页
The composite trapezoidal rule for the computation of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel I/sin2(x- s) is discussed, and the main part of the asymptotic expansion... The composite trapezoidal rule for the computation of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel I/sin2(x- s) is discussed, and the main part of the asymptotic expansion of error function is obtained. Based on the main part of the asymptotic expansion, a series is constructed to approach the singular point. An extrapolation algorithm is presented and the convergence rate is proved. Some numerical results are also presented to confirm the theoretical results and show the efficiency of the algorithms. 展开更多
关键词 hypersingular integrals trapezoidal rule asymptotic error expansion extrapolation algorithm
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The twoscale asymptotic error analysis for piezoelectric problems in the quasi-periodic structure 被引量:1
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作者 FENG YongPing DENG MingXiang GUAN XiaoFei 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2013年第10期1844-1853,共10页
Applications for piezoelectric effect have grown rapidly, and piezoelectric materials play important roles in countless areas of modem life. By means of twoscale method and coupled boundary layer, some new kinds of tw... Applications for piezoelectric effect have grown rapidly, and piezoelectric materials play important roles in countless areas of modem life. By means of twoscale method and coupled boundary layer, some new kinds of twoscale asymptotic expansions for solutions to the electrical potential and the displacement in quasi-periodic structure under coupled piezoelectric effect are derived, and the homogenization constants of piezoelectric materials are presented. The coupled twoscale relation between the electrical potential and the displacement is set up, and some improved asymptotic error estimates are analyzed. 展开更多
关键词 twoscale method PIEZOELECTRICITY quasi-periodic structure homogenization constants
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Error Bounds for Uniform Asymptotic Expansions-Modified Bessel Function of Purely Imaginary Order
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作者 Wei SHI Roderick WONG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2010年第5期759-780,共22页
The authors modify a method of Olde Daalhuis and Temme for representing the remainder and coefficients in Airy-type expansions of integrals.By using a class of rational functions,they express these quantities in terms... The authors modify a method of Olde Daalhuis and Temme for representing the remainder and coefficients in Airy-type expansions of integrals.By using a class of rational functions,they express these quantities in terms of Cauchy-type integrals;these expressions are natural generalizations of integral representations of the coe?cients and the remainders in the Taylor expansions of analytic functions.By using the new representation,a computable error bound for the remainder in the uniform asymptotic expansion of the modified Bessel function of purely imaginary order is derived. 展开更多
关键词 Modified Bessel function of purely imaginary order Airy function Uniform asymptotic expansion Error bound
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