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中文摘要：
在神经传播过程中，神经传递信号及它关于时间和空间的变化率，在数学上表现为一类非线性拟双曲方程．本文在各向异性条件下，讨论了该方程的一个非协调有限元逼近。给出了半离散格式下解关于L^∞（Ⅱ·Ⅱh）模的最优误差估计．利用插值算子与Ritz-Volterra投影的一致性得到了关于神经传递信号的超逼近性质。同时基于插值后处理技术还导出了它的整体超收敛．
英文摘要：
In the nerve conductive process, the nerve transmission signal and its rate of change about the time and the spatial, perform as a class of nonlinear quasi-hyperbolic equations in mathematics. In this paper, a nonconforming finite element is applied to these equations with semidiscretization on anisotropic meshes, the optimal error estimate in L^∞（Ⅱ·Ⅱh） is obtained. The result of superclose about the nerve transmission signal can be acquired by virtue of the property that the interpolation operator is accordance with the Ritz-Volterra projection. At the same time, based on the interpolated postprocessing technique, the global superconvergence is derived.
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