半线性伪双曲方程最低阶的H^1-Galerkin混合元方法

THE LOWEST ORDER H^1-GALERKIN MIXED FINITE ELEMENT METHOD FOR SEMI-LINEAR PSEUDO-HYPERBOLIC EQUATION

研究在半离散和全离散格式下,半线性伪双曲方程最低阶的协调H^1-Galerkin混合有限元逼近.具体地,用双线性元逼近原始变量u,用零阶Raviart-Thomas(R-T)元逼近流量p.首先通过泰勒展式和积分恒等式技巧得到了p的一个新的误差估计式.然后,导出了u在H^1模和p在H(div;Ω)模意义下的超逼近性质,改进了已有文献的结果.

The main aim of this paper is to study the approximation of the low- est order conforming H1-Galerkin mixed finite element （FE） to semi-linear pseudo- hyperbolic equation for semi-discrete and fully-discrete schemes. In detail, the bilinear FE is used to approximate the original variable u and the zero order Raviart-Thomas （R-T） FE to the flux variable p（→）. A new error estimate is firstly established for p（→） through Taylor＇s expansion and integral identity techniques. Then, the superclose properties are deduced for u in Hi-norm and for p（→） in H（div; Ω） norm which improve the results obtained in the existing literature.