【摘要】 在半离散和全离散格式下讨论非线性抛物积分微分方程的类Wilson非协调有限元逼近.当问题的精确解u∈H3(Ω)/H4(Ω)时,利用该元的相容误差在能量模意义下可以达到O(h2)/O(h3)比其插值误差高一阶和二阶的特殊性质,再结合协调部分的高精度分析及插值后处理技术,并借助于双线性插值代替传统有限元分析中不可缺少的Ritz-Volterra投影导出了半离散格式下的O(h2)阶超逼近和超收敛结果.同时分别得到了向后Euler全离散格式下的超逼近性和Crank-Nicolson全离散格式下的最优误差估计.更多还原

【Abstract】 A nonconforming quasi-Wilson finite element approximation for nonlinear parabolic integro-differential equation is discussed under the semi-discrete and fully-discrete schemes.By use of the special property of the element,i.e.,the consistence error estimate in energy norm when the exact solution u of the problem belongs to H3(Ω)/H4(Ω) can reach to O(h2)/O(h3),one/two order higher than the interpolation error,then combination it with the higher accuracy analysis of its conforming part and the interpolated postprocessing technique,the superclose and superconvergence results with order O(h2) are obtained for semi-discrete scheme through interpolation instead of the Ritz-Volterra projection which is an indispensable tool in traditional finite element analysis.The superclose property and the optimal error estimate for backward Euler and Crank-Nicolson fully-discrete schemes are derived,respectively.更多还原