Sobolev方程的扩展特征混合有限元方法  

THE EXPANDED CHARACTERISTICS-MIXED FINITE ELEMENT METHOD FOR SOBOLEV EQUATIONS

作　　者：陈凤欣[1,2] 陈焕贞[2] 

机构地区：[1]山东交通学院数理系,济南250023 [2]山东师范大学数学科学学院,济南250014

出　　处：《高等学校计算数学学报》2010年第4期291-302,共12页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(10971254);山东省自然科学基金(ZR2009AZ003)资助项目;山东省优秀中青年科学家科研基金(2008BS01008)资助项目

摘　　要：对给定的具有光滑边界Γ的区域Ω ＊R^l（l=1,2,3）及时间区间（O,T],考虑如下的对流占优Sobolev方程：In this paper,an expanded characteristics-mixed finite element method is used to simulate Sobolev equations with convection term.The method is a combination of the characteristics line method and the expanded mixed finite element method.The scheme is stable since fluid is transported along the approximate characteristics on the discrete level.At the same time it expands the standard mixed finite element method in the sense that three variables：the scalar unknown, its gradient and its flux are explicitly treated.Moreover,theoretical analysis and numerical example show that the method is stable and its L^2-error estimate is optimal.

关 键 词：SOBOLEV方程 混合有限元方法 特征 光滑边界 时间区间 对流占优 

分 类 号：O241.8[理学—计算数学]