两点边值问题非均匀网格二阶有限体积方法的外推  

The Extrapolation on Second Order Finite Volume Method with Nonuniform Mesh for Two Point Boundary Value Problems

作　　者：王凤[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：《应用数学》2013年第4期900-913,共14页Mathematica Applicata

基　　金：国家自然科学基金资助项目(11071123)

摘　　要：本文针对两点第三边值问题提出非均匀网格二阶有限体积格式的Richardson外推法,导出二阶有限体积格式截断误差的积分形式.通过构造有限体积格式的辅助方程,证明外推法按照离散L2范数,H1半范数,最大范数具有四阶精度.数值算例验证了理论分析的正确性,并说明了外推法的有效性.In this paper, Richardson extrapolation of second-order finite volume scheme on nonuniform mesh is presented for two point boundary value problem of third kind and the truncation errors with integral form are derived. By constructing auxiliary equations corresponding to the finite volume scheme, we .prove that the extrapolation is convergent with fourth order accuracy with respect to discrete L^2, norm, H1 semi-norm and maximum norm. A numerical example verifies the correctness of the theoretical analysis and also shows the effectiveness of the extrapolation.

关 键 词：两点第三边值问题 非均匀网格有限体积方法 RICHARDSON外推法 误差估计 

分 类 号：O241.82[理学—计算数学]