共查询到19条相似文献,搜索用时 336 毫秒
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通过对方程的对流部分采用沿着特征线方向向后两步差分格式进行离散,而对扩散部分采用混合有限元格式进行离散,从而利用多步特征-混合有限元方法对平面非均匀水沙模型进行了数值模拟,给出了相应的误差分析及数值算例. 相似文献
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利用差分流线扩散法和特征有限元方法对二维水沙数学模型进行了数值模拟,并给出了相应的误差分析. 相似文献
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Sobolev 方程的$H^1$-Galerkin混合有限元方法 总被引:6,自引:0,他引:6
对Sobolev方程采用H1-Galerkin混合有限元方法进行数值模拟.给出了一维空间中该方法的半离散和全离散格式及其最优误差估计;并将该方法推广到二维和三维空间.与H1-Galerkin有限元方法相比,该方法不仅降低了对有限元空间的连续性要求;而且与传统的混合有限元方法具有相同的收敛阶,但其有限元空间的选取却不需要满足LBB相容条件.数值例子将进一步说明该方法的可行性与有效性. 相似文献
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研究了针对频域有限元直接动态分析的面向目标误差估计以及误差范围估计计算方法.面向目标的误差估计方法就是专门针对如何准确和经济地估算特定值误差的一种方法,利用原问题的共轭偶问题进行计算.频域有限元的直接动态分析是模拟频域扫描实验的一种计算方法,专门针对谐振激励的线性动态响应问题,利用将原自由度分解为实部和虚部描述频率的变化,从而计算变形体的动态响应.利用扩展针对有限元的面向目标误差估计的自由度,将该方法应用到直接动态分析中进行误差估计.通过建立同时包含实部和虚部自由度的能量弱形式及偶问题,并将其数值实现,估算频域直接动态分析有限元解的误差及误差范围,并通过悬臂梁的激振算例进行了验证. 相似文献
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提出了二维定常Navier-Stokes(N-S)方程的一种两层稳定有限元方法.该方法基于局部高斯积分技术,通过不满足inf-sup条件的低次等阶有限元对N-S方程进行有限元求解.该方法在粗网格上解定常N-S方程,在细网格上只需解一个Stokes方程.误差分析和数值试验都表明:两层稳定有限元方法与直接在细网格上采用的传统有限元方法得到的解具有同阶的收敛性,但两层稳定有限元方法节省了大量的工作时间. 相似文献
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一阶双曲问题的有限元后验误差估计至今没有得到很好的解决.本文对d维区域上一阶双曲问题的k次间断有限元逼近提出了一种新的后验误差分析方法, 进而建立了间断有限元解在DG范数下(强于L2范数)基于误差余量型的后验误差估计. 数值计算验证了本文理论分析的有效性. 本文方法也适用于其他变分问题有限元逼近的后验误差分析. 相似文献
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周艳杰 《数学的实践与认识》2008,38(15)
在已有的对CVD化学方程半离散化和全离散化混合有限元解的存在性及其误差分析的基础上,对其全离散化混合有限元解进行了数值模拟,结果进一步表明了混合有限元解的高精度、易于计算的良好性质. 相似文献
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本征值有限元近似的一个抽象误差估计式 总被引:6,自引:0,他引:6
设T:LZ(fi)MLZ(fi)是自共轭全连续算子,SgCLZ(fi)是分片。次有限元空间,几:LZ、St是有限秩自共轭算子,IITh-Tllo、0(h、0).考虑本征值问题:及其近似用(·,·)和DD·D【。·分别表示h(m中内积和范数·ID·卜F表示w认}(m中范数,简记D卜队。为D卜卜·因为T自共轭全连续,所以它有可数无穷个本征值h,人,...人,....其相应的本征函数(2丹构成完全标准直交系,所以VZELZ(m设几的本征值为A。l,汕。,...,汕n,相应的本征函数为如山,卜则。二1·不失一般性,可EitL。设tik一大干二>,E是到Ah对应的本… 相似文献
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Two-phase miscible flow in porous media is governed by a system of nonlinear partial differential equations. In this paper, the upwind-mixed method on dynamically changing meshes is presented for the problem in two dimensions. The pressure is approximated by a mixed finite element method and the concentration by a method which upwinds the convection and incorporates diffusion using an expanded mixed finite element method. The method developed is shown to obtain almost optimal rate error estimate. When the method is modified we can obtain the optimal rate error estimate that is well known for static meshes. The modification of the scheme is the construction of a linear approximation to the solution, which is used in projecting the solution from one mesh to another. Finally, numerical experiments are given. 相似文献
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三维热传导型半导体问题的交替方向特征有限元方法及理论分析 总被引:1,自引:0,他引:1
1.引言 三维热传导型半导体器件瞬态问题的数学模型由四个非线性偏微分方程描述 [1,2].工程研究中一般考虑绝流边条件,由于绝流条件可以看作一反射条件来处理、为了数值分析方便,我们在此考虑三维周期问题: 其中, =[0,1]3,未知函数是电子位势 ;电子,空穴浓度e,p;温度函数T.方程(1,1)-(1.4)中出现的系数均有正的上下界,且是 周期的. a=Q/ε,Q,ε分别表示电子负荷和介电系数,均为正常数.N(x)是给定的函数.Ds(x)为扩散系数,μs(x)为迁移率,s=e,P.R(e,p,T)… 相似文献
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1.引言多孔介质二相驱动问题的数学模型是偶合的非线性偏微分方程组的初边值问题.该问题可转化为压力方程和浓度方程[1-4].浓度方程一般是对流占优的对流扩散方程,它的对流速度依赖于比浓度方程的扩散系数大得多的Farcy速度.因此Darcy速度的求解精度直接影响着浓度的求解精度.为了提高速度的求解精度,70年代P.A.Raviat和J.M.Thomas提出混合有限元方法[5].J.DouglasJr,T.F.Russell,R.E.Ewing,M.F.Wheeler[1]-[4],[9],[12]袁… 相似文献
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In this article, we study the explicit expressions of the constants in the error estimate of the nonconforming finite element method. We explicitly obtain the approximation error estimate and the consistency error estimate for the Wilson's element without the regular assumption, respectively, which implies the final finite element error estimate. Such explicit a priori error estimates can be used as computable error bounds. 相似文献
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Shipeng Mao Zhong-ci Shi LSEC ICMSEC Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China 《计算数学(英文版)》2009,(4):425-440
In this paper, we study the explicit expressions of the constants in the error estimates of the lowest order mixed and nonconforming finite element methods. We start with an explicit relation between the error constant of the lowest order Raviart-Thomas interpolation error and the geometric characters of the triangle. This gives an explicit error constant of the lowest order mixed finite element method. Furthermore, similar results can be ex- tended to the nonconforming P1 scheme based on its close connection with the lowest order Raviart-Thomas method. Meanwhile, such explicit a priori error estimates can be used as computable error bounds, which are also consistent with the maximal angle condition for the optimal error estimates of mixed and nonconforming finite element methods. 相似文献
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Son‐Young Yi 《Numerical Methods for Partial Differential Equations》2013,29(5):1749-1777
In this article, we develop a nonconforming mixed finite element method to solve Biot's consolidation model. In particular, this work has been motivated to overcome nonphysical oscillations in the pressure variable, which is known as locking in poroelasticity. The method is based on a coupling of a nonconforming finite element method for the displacement of the solid phase with a standard mixed finite element method for the pressure and velocity of the fluid phase. The discrete Korn's inequality has been achieved by adding a jump term to the discrete variational formulation. We prove a rigorous proof of a‐priori error estimates for both semidiscrete and fully‐discrete schemes. Optimal error estimates have been derived. In particular, optimality in the pressure, measured in different norms, has been proved for both cases when the constrained specific storage coefficient c0 is strictly positive and when c0 is nonnegative. Numerical results illustrate the accuracy of the method and also show the effectiveness of the method to overcome the nonphysical pressure oscillations. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
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崔明 《高等学校计算数学学报》2002,24(3):206-211
1 引 言设Ω R2为具有光滑边界的有界区域,考虑非定常的,无量纲化的,而且带有热传导的粘性不可压缩流体力学问题:问题(Ⅰ):求u=(u1,u2),p,T满足: 相似文献
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In this paper, an adaptive finite element method is developed for stationary conduction convection problems. Using a mixed finite element formulation, residual type a posteriori error estimates are derived by means of the general framework of R. Verfürth. The effectiveness of the adaptive method is further demonstrated through two numerical examples. The first example is problem with known solution and the second example is a physical model of square cavity stationary flow. 相似文献