伪抛物型积分微分方程的混合有限元误差估计

基于Raviart-Thomas空间,本文对伪抛物型积分微分方程初边值问题提出了混合有限元方法.与通常的有限元方法相比,该方法可以同时高精度逼近未知函数及未知函数的梯度.通过引入广义混合椭圆投影,证明了其存在唯一性,并得到了其一系列性质,利用其性质给出了平方模范数下的最优误差估计;利用广义混合椭圆投影和正则Green函数得到了最大模范数下的拟最优误差估计.

Error Estimates for Mixed Finite Element Methods for Pseudo-parabolic Intergo-differential Equations

In this paper,a mixed finite element method is proposed to solve the initial-boundary value problem of pseudo-parabolic integro-differential equations.Compared with the usual finite element method,the unknown scalar and the adjoint vector function are approximated optimally and simultaneously.By introducing the projection of generalized mixed element,the existence and unique-ness of projection and some important properties of the projection are proved.By using its properties,the optimal order error estimate...