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中文摘要：
对Possion方程在新的混合变分形式下提出了协调元和非协调元两种逼近格式，并证明了弱强制性条件．进一步地在各向异性网格下利用积分恒等式技巧，得到了有关变量的超逼近性质．同时，通过构造插值后处理算子导出了整体超收敛结果．和通常的有限元格式相比，新格式有如下优势：B—B条件容易证明；总体自由度较少，且低阶协调元格式是目前自由度最少的矩形元格式，可以导出比通常高一阶的收敛效果．
英文摘要：
A conforming finite element and a nonconforming finite element schemes of Possion equations are persented based on a new mixed variational form, then the weak coercivity of this form is established. Furthermore, through integral identity techniques the superclose properties of the related variables are derived under anisotropic meshes. At the same time, the global superconvergence is obtained by constructing the interpolation post-processing operator. In contrast to other mixed finite element schemes, new schemes have some advantages： the B-B condition is easy to be proved; fewer degrees of freedom is involved and the lowest order conforming rectangle element is the simplest rectangle element so far; one order higher convergence results than that of the conventional analysis can be derived.
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