非线性抛物型积分微分方程有限元方法的插值后处理技术

THE INTERPOLATED POSTPROCESSING TECHNIQUE OF THE F.E.M. FOR NONLINEAR PARABOLIC INTEGRODIFFERSNTIAL EQUATIONS

本文以两类非线性抛物型积分微分方程为例，首次尝试将插值后处理思想［１］应用到非线性发展型方程上，获得了半离散和全离散有限元解，经插值后处理之后在Ｌ∞（Ｈ１）；Ｌ∞（Ｌ２）模意义下，整体超收敛１阶的高精度，并且计算量没有因此而增加．本文引进并证明较文［２］更广泛的一类椭圆Ｈ１－Ｖｏｌｔｅｒｒａ投影的Ｈ１；Ｌ２，Ｈ－１模最优估计．本文的分析方法可在各类发展型微分及积分微分方程上面通用．

This paper studies the application of interpolated postprocessing tecboque to nonlinear parabolic integrodmereatial equations, and obtains the global superconvergence of first order for senddiscrete and fully discrete F.E.M. scheme's error estimates. The methods of this paper are generally applicable to the nonlinear differelltial and integrofferential equations of evolution.