本文第一部分主要考虑在各向异性网格下用矩形单元对二维空间中二阶椭圆边值问题进行逼近。
Two kinds of rectangular elements are considered to solve the two-dimensional and second-order elliptic boundary value problem on anisotropic meshes.
本文主要考虑在一类各向异性网格(我们称之为gatm)下用一些三角形单元逼近二维空间中二阶椭圆边值问题。
Some triangular elements are considered to solve the two-dimensional and second-order elliptic boundary value problem on a class of anisotropic meshes (we call them GATM).
本文针对一维和二维双曲型方程的初边值问题，设计了几类高效率串行格式和并行算法。
In this paper, I design a series of high-efficiency serial schemes and parallel algorithms for one-dimension and two-dimension hyperbolic equation.
本文使用矩方法处理了具有随机初始条件的一维波动方程的第一边值问题。
In this paper, moment method is used to deal with the first boundary value problem of one dimensional wave equation with stochastic initial and boundary conditions.
讨论具有一般形式的对流项、扩散项、边界流项以及反应项的一维牛顿渗流方程初边值问题非负解的整体存在性。
The present paper studied the global existence of nonnegative solutions of one-dimensional Newtonian filtration equation with more general boundary fluxes term, reaction, diffusion and convection.
本文研究拖索稳态理论的三维问题，建立了微分方程，提出了一个简便的积分方法，并且用优化方法处理与此相联系的边值问题。
The three-dimensional steady state theory of towing cable is studied, with differential equations derived and a simple method of integration suggested.
进一步在边界层区域将三维的边值问题分解成二维的平面应变和扭转问题。
Furthermore, the 3-d boundary value problem in boundary layer region is decomposed to 2-d plane strain and torsion problems.
本文讨论了在一维情况下一类非牛顿流初边值问题整体解的存在唯一性。
In this paper, we prove the existence and uniqueness of global weak solution of non Newton Filtration equation with a kind of nonlinear boundary condition.
本文讨论了一类具有较强应用背景的二维半线性伪抛物方程，设计了求解此类方程对应的初边值问题的隐式差分格式。
A type of 2D semi-linear pseudo-parabolic equation is cousidered, which has wide application areas. An implicit difference scheme corresponding to the IBVP of this equation is designed.
第五章讨论二维蜂窝结构热方程边值问题，给出了一个多尺度渐近展开式和有限元计算格式。
In Chapter 5, we study the multi-scale finite element method for the heat equation of composite materials with honeycomb structure in two dimension domain.
另一方面，采用传统迭代子和共轭梯度法作为光滑子，我们证明了瀑布型多重网格法对一、二维非线性椭圆边值问题，在能量范数下，均可获得最优收敛阶。
Onthe other hand, with traditional iterations and the conjugate gradient(CG) as smoothers, we can show the optimal convergence rate of the cascadic method in energy norm for 1-D and 2-D cases.
研究了一维线性标量守恒律初边值问题的弱解，分析了有限元方法的收敛性。
In this paper, a finite element method for linear scalar conservation laws is analyzed.
研究了一维线性标量守恒律初边值问题的弱解，分析了有限元方法的收敛性。
In this paper, a finite element method for linear scalar conservation laws is analyzed.
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