Moreover, for a parabolic variational inequality, we also propose a domain decomposition method for the Euler-Galerkin approximation of a parabolic variational inequality. It is proved that the convergence rate of the algorithm is independent of the space meshsize h and the time stepsize.
本文还研究了一类抛物型变分不等式区域分解算法，证明了算法的收敛性且收敛不依赖于空间格子尺寸以及时间步长。
In order to study the migrating rule of contaminants, a steady two dimentional mathematical model is adopted to simulate the groundwater flow field around the uranium miffing dam, and the model is solved with Galerkin finite element method.
为了研究污染物在地下水中的迁移规律，采用二维稳定流数学模型对铀尾矿库周围地下水流场进行概化，并用Galerkin有限元法对模型进行了求解。
Semi-analytical finite element method is applied to reduce the hydroclashc problemof the fluid filled spherical tank with damping spherical shell to two dimensionalproblem, the Gaerkin method and Hamilton principle is used respectively to productthe system equation of flind and dampng spherical shell.
本文根据对称性采用半解析有限元法，将带有球形弹性隔板的球形贮箱中的三维流弹耦合问题化为两维问题。对流体域采用三角形环单元，球壳隔板采用截锥单元，分别应用Galerkin方法和Hamilton原理对流体和球壳隔板推导出了有限元离散方程。
It is considered that the fluid can be modeled as a viscoelastic medium with equivalent Lame constant. In addition, for thin layer at low frequencies, the porous frame may be assumed as motionless. In this case, the reduced control equation of pore fluid in porous material is obtained by Biot's theory. Similarly, the pore fluid is also equivalent to an elastic medium. The finite element formulation is derived by using the Galerkin technique. The influences of the fraction of porous medium, the material constants of pore fluid in porous medium of the inhomogeneous layer, the layer thick and different arrangements of inhomogeneous layers on the reflection characteristics of the structure were analyzed.
文中将流体等效处理为弹性体；对多孔介质，提出在薄层、低频下忽略其骨架的运动，由Biot理论获得退化的孔中流体的基本方程，并将其等效处理为弹性体；利用Galerkin方法建立了有限元方程，分析了非均匀层中多孔介质的体积分数，孔中流体材料参数、层厚度及多层非均匀介质的不同迭合对其结构反射特性的影响。
First of all, the basis of the MRTD method is studied. In Chapter 2, wavelets analysis and multiresolution analysis, the mathematical basis, are introduced, and the characteristics of the wavelets basis functions, including orthonormality, compact support, multiresolution and so on, are also introduced. The advantages of the applications of these functions to the numerical electromagnetic calculations are discussed. In Chapter 3, the algorithm basis of MRTD: the combination of the wavelets and the method of moments is studied. This Chapter shows that the MoM based MRTD method is the combination of wavelets and MoM using Galerkin sampling.
文中首先讨论了 MRTD 的建立基础，其中第二章介绍了其数学基础－小波分析及多分辨分析，讨论了小波基函数的性质包括正交性、紧支撑性、多分辨性等及其应用于电磁场数值计算的优势；第三章讨论了其算法基础－小波与矩量法的结合，阐述了以矩量法作为算法基础，以 Galerkin 离散采样的方式与小波函数结合而产生了 MRTD。
The results are good for the application of the Element-free Galerkin Method in the seismic forward modeling.
以上分析结果，对无单元Galerkin法在地震波正演模拟中的应用具有一定的指导意义。
First, the planar waveguide models for Rotman lens and its feed lines which incorporate the dispersion effect with frequencies are set up. Then the aperture electric fields at lens ports are expanded by appropriate waveguide mode functions and substituted into the contour integral equation. The multimode scattering matrix of the lens can be acquired by solving the contour integral equation by using Galerkin method.
首先建立了考虑色散效应的透镜的等效平板波导模型，然后选择适当的波导模式函数展开透镜端口上的场，并利用Galerkin法求解其边缘上电场满足的轮廓积分方程即可得到透镜的多模式散射参数。
First of all, Cauchy inequality is used to obtain a basic inequality. Secondly, the functions of basis are made by Galerkin method, and the error estimates of eignevalues are obtained by Cauchy inequality. At last, the computational method of the approximate value of the eigenvalues turns out immediately, and accuracy of the-th approximate value is estimated by the n-tb approximate value.
首先利用Cauchy场不等式证明了一个基本不等式；其次采用Galerkin方法来构造适当的基函数，并利用Cauchy不等式给出了其特征值计算的误差佑计式；最后得到计算梁横向振动问题的特征值的近似值的算法，而且可以用第n次近似值来估计第n-1次的近似值的精确度。
A rigid-plastic element-free Galerkin-finite element coupling method was developed for the numerical simulation of plane lateral extrusion process.
应用刚塑性耦合无网格-有限元法，对平面侧向挤压过程进行数值模拟。
In order to evaluate the water resources of the whole drainage area of Heilongdong, the pape establishes groundwater seepage model of the whole spring area of Heilongdong through the in-depth research of geological condition and the date of water level of this area based on water balance theory, groundwater seepage flow theory and Galerkin finite element theory.
为了对黑龙洞泉域水资源进行评价，通过对地质条件、水位观测资料的深入研究，以水均衡原理、地下水渗流理论为基础，建立了黑龙洞泉域地下水渗流数值模型。
By using the Galerkin method, the partial differential equation was transformed into ordinary one, which was solved with L-P method.
通过Galerkin方法将偏微分程转化为常微分方程，采用L-P法对常微分方程进行求解。
By the Galerkin method, the partial differential equation was transformed into ordinary differential equation and then solved with L-P method and KBM method.
通过Galerkin方法，将偏微分程转化为常微分方程，并采用L-P法及KBM法对常微分方程进行了求解。
Finally, The finite dimensions dynamic equations considering the rigid-elastic coupling effects were obtained by taking advantage of Galerkin method, and the validity of the theories presented in this paper was verified by a numerical simulation example.
最后采用Galerkin方法对其离散化，导出有限维离散化动力学模型，并给出仿真算例，验证了该模型的正确性。
In this paper, the Galerkin method is used to solve the Laplace-Young equation for calculation of simplified monodisperse emulsion system to obtain the relationship among mean curvature, contact angle, volume fraction, fractional fil...
获得了平均曲率、接触角、体积分数、接触面积分数、单位体积界面积等参数之间的关系，并提出了接触角不为零时的渗透压表达式。
In this system, Galerkin meshless method based moving least square approximation is applied in space coordinate domain.
无网格方法是近年来受到广泛关注的微分方程求解技术。
The most typical characteristic of MLPG is that it involves only integration on a local subboundary centered and over a regular local subdomain at the node. Moreover, it was stated that recent developments and applications of MLPG methods were presented.
此方法的最大特点是在所考虑点处的规则局部区域上以及局部边界上积分，同时给出了建立在无网格局部Petrov-Galerkin方法基础之上的几种MLPG方法，以及MLPG方法的进展和应用。
The dynamic boundary condition is redused to a weighted residual equation by employing the Galerkin nethod.
对于自由液面的非线性动力边界条件，应用Galerkin加权方法进行了有限元数值离散。
The three-dimension alternative electromagnetic field of square billet soft-contact mold was simulated by using the Galerkin finite element method.
摘 要：运用Galerkin有限元法对方坯软接触结晶器内三维交变磁场进行了数值模拟。
Adall[1], it is verified that Galerkin-finite strip method iseffective in solving this kind of problems.
Adall的结果［1］的比较，证明了Galerkin—有限条法是解决此类问题的一种行之有效的方法。
The Galerkin-finite strip method which is used to solve the flutter problems of plates is proposed.
提出了一种求解板的颤振失稳问题的Galerkin—有限条法。