非线性粘弹性方程的EQ_1^(rot)非协调有限元分析(英文)  

EQ_1^(rot) Nonconforming Finite Element Analysis for Nonlinear Viscoelasticity Equations

作　　者：王芬玲[1] 赵艳敏[1,2] 石东洋[2] 

机构地区：[1]许昌学院数学与统计学院,河南许昌461000 [2]郑州大学数学系,河南郑州450025

出　　处：《应用数学》2013年第1期1-10,共10页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(10971203,11101381);the Natural Science Foundation of Henan Province(112300410026);the Natural Science Foundation of the Education Department of Henan Province(12A110021,2011A110020)

摘　　要：针对非线性粘弹性方程,在半离散和全离散格式下给出EQ1rot非协调有限元逼近.由于该单元的相容误差 (O(h2)阶)比插值误差 (O(h)阶)高一阶,可得到在H1模意义下的O(h2)阶超逼近结果,并利用插值后处理技术导出整体超收敛.进而,基于该单元的渐近展开式,构造新的插值后处理算子和外推格式,给出O(h4)阶的外推结果.最后,运用与以往文献不同的方法得到全离散逼近格式的最优误差估计.EQrot/1 nonconforming finite element approximation to a class of nonlinear viscoelasticity e- quations is discussed for semi-discrete and fully-discrete schemes. Since the consistency error of this element is of order O（h2 ） which is one order higher than its interpolation error O（h）, the superclose result of order O（h2） in broken H1 -norm is obtained. And then, the global superconvergence is de duced by interpolation postprocessing technique. Moreover, the extrapolation result of order O（h4） is derived by constructing a new interpolation postprocessing operator and extrapolation scheme base on the asymptotic expansion formulas of this element. Finally, the optimal error estimate is gained for a proposed fully-discrete scheme with helo of different approaches from the previous literature.

关 键 词：非线性粘弹性方程 EQ1rot非协调有限元 超逼近和超收敛 外推 半离散和全离散格式 

分 类 号：O242.21[理学—计算数学]