伪双曲积分微分方程的半离散混合元法误差估计

Error Estimates Using a Semi-discrete Mixed Element Method for Pseudo-hyperbolic Integro-differential Equations

运用混合有限元方法研究了一类伪双曲型积分微分方程初边值问题基于Raviart-Thomas空间Vh×Wh的L2,L∞的误差估计.与通常的有限元方法相比,该方法可以同时高精度的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,给出了未知函数u,ut,utt,伴随速度σ和散度divσ逼近解的最优阶L2误差估计,并且还得到了u及σ逼近解的L∞误差估计.

A mixed finite element method is proposed to investigate the convergence of the initial-boundary value problem of pseudo-hyperbolic integro-differential equations based on the Raviart-Thomas space Vh× Wh.Compared with the usual finite element method,the unknown scalar and the adjoint vector function are approximated optimally and simultaneously with this method.By introducing the projection of generalized mixed elements,optimal order L2 estimates are obtained for the approximation of unknown functions u,ut,utt,the associated velocity σ and divσ.L∞ estimates are also obtained for the approximations of u and σ.