伪抛物型积分微分方程的混合有限元误差估计

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

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。

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 uniqueness of projection and some important properties of the projection are proved. By using its properties, the optimal order error estimates in square norm are derived; By using the projection of generalized mixed element and the regular Green function, quasi-optimal order error estimates in maximal norm are finally obtained .