共查询到17条相似文献,搜索用时 31 毫秒
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二阶椭圆问题新的混合元格式 总被引:2,自引:0,他引:2
本文基于二阶椭圆问题一种新的混合变分形式,给出同时满足强椭圆性和B-B条件的任意次的求解格式.理论分析表明这些单元论证简单而且用了较少的自由度达到最优误差估计.同时我们还给出了它们在各向异性网格下的误差估计. 相似文献
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《数学的实践与认识》2013,(23)
将Nedelec J C所提出的三棱柱单元构造方式运用到Poisson方程,利用Raviart、Thomas所提出的混合元变分形式,并利用Fortin准则证明了离散BB条件,最后给出了误差估计. 相似文献
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《数学的实践与认识》2015,(22)
对二阶椭圆问题构造了一个非常规各向异性Hermite型矩形单元.并基于泡函数对其构造了一种简化的稳定化混合元格式.同时给出了格式的收敛性分析和后验误差估计. 相似文献
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基于Lagrange乘子法的一种二阶椭圆问题混合元格式 总被引:2,自引:0,他引:2
本文利用Lagrange乘子法的思想,修改了传统的混合变分形式,将二阶椭圆问题转化为与其等价的新的变分形工,给出了针对该新形式进行离散求解的一种混合元格式,与现在已知格式相比,用较少的自由度获得了较高的逼近阶。 相似文献
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本文利用正规格林函数及对偶论证技术证明了一类强非线性二阶椭圆问题混合方法对函数的L^2投影具有几乎超收敛一阶的最大模误差估计,对伴随向量函数具有拟最优最大模误差估计。 相似文献
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1.引 言 令 是有界区域,边界 充分光滑.Sobolev空间 是熟知的.引入Q= H(div;Ω),U= H1(Ω),内积和范数记为而 是 的半范.令 ,其范数为 . 考虑如下二阶椭圆问模型题:由问题(0.1)的位移有限元解通过求导的方法来求p的近似解,会带来额外的舍入误差.应用Babuska-Brezzi混合元法[2]则可得到p足够精度的逼近解.但是,该方法要求离散K-椭圆性和Inf-Sup不等式同时成立,使得混合元的构造或自由度的选取变得相当复杂[2,12-14].通过“增补”办法,能够克服K-椭圆性… 相似文献
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This paper studies second-order optimality conditions for a semilinear elliptic optimal control problem with mixed pointwise constraints. We show that in some cases, there is a common critical cone under which the second-order necessary and sufficient optimality conditions for the problem are valid. Our results approach to a theory of no-gap second-order conditions. In order to obtain such results, we reduce the problem to a special mathematical programming problem with polyhedricity constraint set. We then use some tools of variational analysis and techniques of semilinear elliptic equations to analyze second-order conditions. 相似文献
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Lung’an YING 《数学年刊B辑(英文版)》2007,28(4):441-452
The author studies the structure of solutions to the interface problems for second order linear elliptic partial differential equations in three space dimension.The set of singular points consists of some singular lines and some isolated singular points.It is proved that near a singular line or a singular point,each weak solution can be decomposed into two parts,a singular part and a regular part.The singular parts are some finite sum of particular solutions to some simpler equations,and the regular parts are bounded in some norms,which are slightly weaker than that in the Sobolev space H~2. 相似文献
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Regular solutions to second-order elliptic systems on the plane are representable in terms of A-analytic functions satisfying an operator equation of the Beltrami type. We prove Carleman-type formulas for reconstruction of solutions from data on a part of the boundary of the domain. We use these formulas for solving the Cauchy problems for the system of Lame equations, the Navier–Stokes system, and the system of equations of elasticity with resilience. 相似文献
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In this paper, a new hybridized mixed formulation of weak Galerkin method is studied for a second order elliptic problem. This method is designed by approximate some operators with discontinuous piecewise polynomials in a shape regular finite element partition. Some discrete inequalities are presented on discontinuous spaces and optimal order error estimations are established. Some numerical results are reported to show super convergence and confirm the theory of the mixed weak Galerkin method. 相似文献
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In a semi-infinite cylinder, we consider the behavior of generalized solutions of second-order divergence-form elliptic equations satisfying the third boundary condition on the lateral surface of the cylinder. 相似文献
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Madhusmita Tripathy 《Numerical Functional Analysis & Optimization》2013,34(3):320-337
We derive superconvergence result for H 1-Galerkin mixed finite element method for second-order elliptic equations over rectangular partitions. Compared to standard mixed finite element procedure, the method is not subject to the Ladyzhenskaya–Bab?ska–Brezzi (LBB) condition and the approximating finite element spaces are allowed to be of different polynomial degrees. Superconvergence estimate of order 𝒪(h k+3), where k ≥ 1 is the order of the approximating polynomials employed in the Raviart–Thomas elements, is established for the flux via a postprocessing technique. 相似文献