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中文摘要：
在这份报纸， nonconforming quasi-Wilson 到非线性的 sine-Gordan 方程的一个班的有限元素近似被讨论。从存在文学基于双线性的元素和不同技术的已知的更高的精确性结果，它被证明内部产品(?( u - Ih1u )，? vh )并且一致性错误能在破 H1 作为顺序 O ( h2 )被估计- norm/L2 -标准什么时候 u 鈭? H3 (惟) /H4 (惟)在 Ih1u 是 u 的双线性的插值的地方， vh 属于 quasi-Wilson 有限元素空间。同时，有为在概括矩形的网孔下面的半分离的计划的顺序 O (h2 ) 的 superclose 结果被导出。而且，一个充分分离的计划被建议，顺序 O ( h2 + 蟿2 )的相应错误估计为矩形的分区被获得什么时候 u 鈭? H4 (惟)，它比 nonconforming 上的平常的分析的高象有 ADI 计划和一份订单的双线性的元素的一样一样有限元素。[从作者抽象]
英文摘要：
In this paper, nonconforming quasi-Wilson finite element approximation to a class of nonlinear sine-Gordan equations is discussed. Based on the known higher accuracy results of bilinear element and different techniques from the existing literature, it is proved that the inner product △↓（u - Ih^1u）, △↓vh） and the consistency error can be estimated as order O（h^2） in broken H^1 - norm/L^2 - norm when u ∈ H^3（Ω）/H^4（Ω）, where Ih^1u is the bilinear interpolation of u, Vh belongs to the quasi-Wilson finite element space. At the same time, the superclose result with order O（h^2） for semi-discrete scheme under generalized rectangular meshes is derived. Furthermore, a fully-discrete scheme is proposed and the corresponding error estimate of order O（h^2 ＋ τ^2） is obtained for the rectangular partition when u ∈ H^4（Ω）, which is as same as that of the bilinear element with ADI scheme and one order higher than that of the usual analysis on nonconforming finite elements.
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