两点边值问题基于三次混合插值的超收敛有限体积元方法  

Superconvergent finite volume element method for mixed two point boundary value problems based on mixed cubic interpolations

作　　者：周磊[1] 王同科[1] 

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《天津师范大学学报（自然科学版）》2013年第1期13-19,共7页Journal of Tianjin Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11071123)

摘　　要：针对两点混合边值问题提出了基于三次混合插值的超收敛有限体积元方法,该方法形成的线性代数方程组具有五对角性质,可以使用带状消去法求解.证明了格式按照离散H1半范数具有四阶收敛精度.最后,通过数值算例验证了结论的正确性.A superconvergent finite volume element method for mixed two point boundary value problems based on mixed cubic interpolations is presented. The linear algebraic system derived by the scheme has pentadiagonal property and can be solved by band elimination method. It is proved that the given scheme is convergent with fourth-order accuracy according to HI discrete seminorm. Finally a numerical example is given to show the correctness of theoretical analysis of the scheme.

关 键 词：两点混合边值问题 三次混合插值 超收敛有限体积元方法 误差估计 

分 类 号：O241.82[理学—计算数学]