First , we present the equivalent variatial formulations of the least - squares mixed method and prove the existence and uniques for the weak problems . on the basis of l2 - projections and raviart - thomas projections , we obtain the superconvergence of the least - squares mixed finite element approx - imations on uniform triangulations , where triangular mixed finite elements of the lowest order raviart - thomas spaces are used to approximate the flux p . in the second chapter , we briefly recall the standard and mixed finite methods for second order elliptic problems , and introduce a modified least - squares mixed method 作者首先导出了最小二乘混合元方法的等价变分形式，并且证明了变分问题广义解的存在唯一性；在此基础上，我们采用强一致三角形剖分，选取最低阶的raviar - thomas空间对未知函数的通量进行逼近，利用l ~ 2投影和raviart - thomas投影，得到了插值投影和最小二乘混合元解之间的超收敛结果。
In this context a genetic algorithm ( ga ) was applied to the four - dimension ( 4 - d ) variational data assimilation , which provided a kind of new and effective method in the initial field optimization . the theoretical basis and detailed algorithm were introduced in this paper . at the same time , according to the property of the variational problem itself , we designed the rational genetic coding , operators and parameters 本文将遗传算法应用于四维变分资料同化问题，提供了一种新的较为有效的nwp初始场优化方法，给出了相应的理论依据和详细算法，并结合变分问题本身的特点，设计了合理的遗传编码、遗传操作和遗传参数。
Based on this milti - hierarchical model , application method for information organization of part is presented . chapter 3 proposes a new rule of arbitrary maximum angles of chord for triangulation and locale optimum , which avoides calculating angles of conventional methods in mesh simplification . moreover , with the introduction of arithmetical average windage concept , optimum method for the boundary mesh retriangulations is presented 第三章针对曲面网格简化操作过程中出现的空洞剖分问题，讨论层次模型的网格优化方法，提出了基于弦内角最大准则的局部网格简化方法；针对网格曲面上存在的曲折边界缺陷，提出以边界轮廓算术平均偏差作为边界曲折程度评定参数的边界平滑优化剖分方法。
