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中文摘要：
对二阶椭圆特征值问题，提出一种新的总体自由度到目前为止最少的低阶矩形元格式，给出特征值和特征函数的收敛性分析和误差估计．另一方面，通过引入混合元投影算子和利用积分恒等式技巧得到特征值误差的一个渐近展开式，并由此构造出特征值的外推解，将其收敛精度提高了一阶．
英文摘要：
A low order rectangular finite element scheme with the smallest total degrees of freedom so far is presented for second order eigenvalue problem, then the convergence a- nalysis and error estimates of eigenvalue and eigenfunction are derived. On the other hand,by employing mixed finite element projection operators and using the technique of integral iden- tities,asymptotic error expansion for eigenvalue is obtained, which leads to the construction of the extrapolation solution of eigenvalue,and improves the accuracy by one order.
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