一类非线性四阶双曲方程一个低阶混合元方法的超收敛分析

Superconvergence Analysis of a Lower Order Mixed Finite Method for a Type of Nonlinear Fourth-order Hyperbolic Equations

对一类非线性四阶双曲方程利用双线性元Q_(11)给出一个低阶混合元逼近格式.利用双线性元的高精度结果,关于时间t的导数转移技巧,插值与投影相结合的思想及分裂技术,在半离散格和全离散式下,分别导出原始变量u和中间变量v=-?u在H^1模意义下具有O(h^2)/O(h^2+τ~2)阶的超逼近性质.与此同时,借助插值后处理技术,证明在H1模意义下具有O(h^2)/O(h^2+τ~2)阶的整体超收敛结果.这里,h和τ分别表示空间剖分参数和时间剖分参数.

Based on the bilinear element Q_（11）,a lower order conforming mixed finite element scheme is proposed for a type of nonlinear fourth-order hyperbolic equations.With the help of the known high accuracy results of bilinear element,derivative delivery technique of time t,the error estimate between interpolation,Ritz projection and splitting skills,the superclose properties with order O（h^2）/O（h^2＋τ~2） of original variable u and intermediate variable v =-？u in H^1-norm are derived for semi-discrete and fully-discrete schemes,respectively.Meanwhile,through interpolated postprocessing approach,the global superconvergence results of the above variables with order O（h^2）/O（h^2＋τ~2） in H^1-norm are proved.Here,h and τ are parameters of subdivision in space and time step,respectively.