【摘要】 Zenisek等人给出了窄边四边形上的双线性插值定理 ,但是误差估计式中的常数不是最优的 .首先给出Poincar啨不等式和?坏仁降母慕问?,并通过证明过程的精细估计 ,给出了窄边四边形插值定理优化形式 ,优化定理中的常数比原来相应常数小得多 (约为原来常数的 1/ 2～ 1/ 5 ) .更多还原

【Abstract】 The interpolation theorem for narrow quadrilateral isoparametric finite element was presented by A.Zenisek and M.Vanmaele.But the constants in error estimates are not optimal.The improved forms of Poincaré inequality and trace inequality are provided.And the optimized interpolation theorem for narrow quadrilateral is given through careful estimate of the proof process.The constants of optimized theorem are much less than the original ones.It is about 1/2～ 1/5 of the orginal ones.更多还原