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中文摘要：
针对定常扩散问题,在非结构四边形网格下,通过选取特殊的控制体和有限体元空间,建立两种保对称有限体元格式,在拟一致网格剖分下,当扩散系数光滑时,证明有限体元解函数在L2和H1范数下均具有饱和误差阶.数值实验验证理论结果的正确性,同时表明新格式对扭曲大变形四边形网格、间断系数问题具有较强的适应性.在正交网格下,第二种格式对流（flux）函数在单元中心点的值还具有超逼近性.
英文摘要：
With special control volumes and finite volume element spaces, two symmetry-preserving finite volume element schemes for stationary diffusion problems are established on unstructured quadrilateral grids. Saturated order of error in L2-norm and Ht -norm for discrete solutions under quasi-uniform partition is demonstrated as diffusion coefficient is smooth. Numerical examples verify theoretical results. It shows strong adaptability of the scheme on distorted quadrilateral grids and for diffusion problems with non-smooth coefficient. The second scheme shows super-approximation for flux function at central point of element as grids are orthogonal.
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