一维奇异抛物方程的混合有限元方法  

MIXED FINITE ELEMENT METHOD FOR ONE-DIMENSIONAL SINGULAR PARABOLIC EQUATION

作　　者：白阿拉坦高娃[1] 何斯日古楞 李宏 

机构地区：[1]赤峰学院数学与统计学院,赤峰024000 [2]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《高等学校计算数学学报》2015年第4期289-301,共13页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(11361035);内蒙古自然科学基金(2014BS0101)

摘　　要：1引言 本文利用混合有限元方法考虑一维奇异抛物问题In this paper, mixed finite element method for one-dimensional singu- lar parabolic problem is studied. Semi-discrete scheme and fully-discrete scheme combined with Euler backward difference scheme are constructed. The error es- timates in weighted L2-norm and weighted Hi-norm for the schemes are proved. Numerical examples are given to confirm the theoretical results. The numerical difficulties brought from the singularity are overcome effectively by the application of the sparse grid method near the singular point, and a better simulation result is obtained.

关 键 词：混合有限元方法 奇异抛物方程 一维 抛物问题 

分 类 号：O241.8[理学—计算数学]