非线性S-G型湿气迁移方程的H^1-Galerkin混合元方法  

H^1-Galerkin Mixed Finite Element Method for Nonlinear Sobolev-Galpern Type Equations of Moisture Migration

作　　者：罗娟[1] 张厚超[1] 王俊俊[1] 

机构地区：[1]平顶山学院数学与信息科学学院,河南平顶山467000

出　　处：《山西大学学报（自然科学版）》2016年第2期196-203,共8页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(11271340)

摘　　要：利用双线性元和零阶Raviart-Thomas(R-T)元对非线性Sobolev-Galpern型湿气迁移方程建立了H1-Galerkin混合有限元格式,证明了逼近格式解的存在唯一性。借助双线性元已有的高精度分析,平均值技巧和插值后处理算子,导出精确解u在H1模及中间变量p在H(div;Ω)模意义下的超逼近性质和整体超收敛结果。同时,应用积分恒等式技巧对零阶R-T元进一步导出一个新的误差渐进展开式,得到O(h3)阶的外推解(这里h是剖分参数)。Employing bilinear element and zero-order Raviart-Thomas element（R-T）,H1-Galerkin mixed element schem is established for nonlinear Sobolev-Galpern type equations of moisture migration.The existence and uniqueness of the solution about the approximation scheme are proved.With the help of the known high accuracy analysis of the bilinear,mean-value technique and interpolated postprocessing operators,the superclose properties and the global superconvergence results of exact solution uin H1-norm and intermediate variable pin H（div;Ω）-norm are deduced.Furthermore,a new high asymptotic error expansion is deduced by use of integral identity technique with zero-order Raviart-Thomas element（R-T）and the extrapolation solution with order O（h3）is obtained（here his the meshing partition）.

关 键 词：非线性湿气迁移方程 H1-Galerkin 超逼近和超收敛 外推 

分 类 号：O242.21[理学—计算数学]