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中文摘要：
用标准有限元求解椭圆边值问题,特别是含有多个变量的偏微分方程组时,由标准方法推导出的变分问题经常会出现鞍点问题,这将使得对应的离散化的代数问题是无限维的,给数值求解带来巨大困难;最小二乘有限元方法不会出现鞍点问题,但是在求解时,其产生大的半带宽会带来更大的运算量及求解结果的不精确;为解决上述问题,并取得最佳逼近解,给出了线弹性平板问题的两步最小二乘有限元方法,并对该方法进行了数值分析,并通过算例,验证了该方法的正确性。
英文摘要：
When elliptical boundary value problems which specially include multi-variable are solved by standard finite element,their variation often occur saddle-point problem which make discrete algebra problem be infinite dimension,so numerical approximation is very difficult.Least-square finite element is not needed to subject LBB condition,due to generating larger semi-bandwidth induce numerical solution inaccuracy.In order to avoid this problem and get optimal approximation numerical solution,in this paper,we give two step least-square finite element algorithm for linear elastic problem,and do numerical analysis for this scheme.Then by numerical test,the method is valid.
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