CAJ | 학술논문

利用双线性元和 Nédélec＇s 元，对广义神经传播方程建立了最低阶自然满足 Brezzi-Babuka 条件的新混合元逼近格式。基于该混合元的高精度分析和插值后处理算子技术，在半离散格式下分别导出了原始变量的 H 1模及中间变量的 L2模的超逼近性质和整体超收敛结果。当 f（u）＝f（X）时建立了一个具有二阶精度的全离散逼近格式，分别得到了原始变量的 H1模的超逼近性和中间变量的 L2模的最优误差估计。
이용쌍선성원화 Nédélec＇s 원，대엄의신경전파방정건립료최저계자연만족 Brezzi-Babuka 조건적신혼합원핍근격식。기우해혼합원적고정도분석화삽치후처리산자기술，재반리산격식하분별도출료원시변량적 H 1모급중간변량적 L2모적초핍근성질화정체초수렴결과。당 f（u）＝f（X）시건립료일개구유이계정도적전리산핍근격식，분별득도료원시변량적 H1모적초핍근성화중간변량적 L2모적최우오차고계。
A lowest order new mixed element approximate scheme with the bilinear element and Nédélecc's element for the generalized nerve conductive equations is proposed,which can satisfy Brezzi-Babuka condition automatically. Based on high accuracy analysis of the mixed element and interpolation post-processing technique,the superclose prop-erties and superconvergence results of original variable in H 1 -norm and intermediate variable in L2-norm are deduced separately for semi-discrete scheme.At the same time,a second order fully-discrete scheme when is f(u)equal to f(X) is established and the superclose properties and the optimal order error estimates of original variable in H1 -norm and in-termediate variable in L2-norm are separately derived.