二次有限元解的渐近展开与外推  

ASYMPTOTIC EXPANSION AND EXTRAPOLATION FOR QUADRATIC FINITE ELEMENT

作　　者：吕涛[1] 朱瑞[1] 

机构地区：[1]四川大学数学学院,成都610064

出　　处：《系统科学与数学》2008年第3期340-349,共10页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(10671136);教育部博士点基金资助课题.

摘　　要：在Poisson方程的求解域Ω存在一致的三角剖分,并且相邻两初始单元构成平行四边形的假设下,证明了若Poisson方程的解u属于H^6(Ω),那么二次有限元的误差有h^4的渐近展开.基于误差的渐近展开,可以利用h^4-Richardson外推进一步提高数值解的精度阶,并且能够得到一个后验误差估计.最后,一个数值算例验证了理论分析.Suppose that there exists a uniform triangular partition on the domain Ω, and two adjacent elements form a parallelogram, then it is Proven that approximation error of quadratic finite element has asymptotic expansion with power h^4, if solution u of Poisson equation belongs to H^6（Ω）. By virtue of ha-Richardson extrapolation based on the asymptotic expansion, the authors not only the accuracy order of the approximation is improved, but also a posteriori error estimation is given. A numerical example demonstrates these theoretical results.

关 键 词：二次有限元 渐近展开 外推 后验估计 

分 类 号：O241.82[理学—计算数学]