拋物型界面问题的变网格有限元方法

FINITE ELEMENT METHODS WITH MOVING GRIDS FOR PARABOLIC INTERFACE PROBLEMS

本文针对抛物型界面问题,提出了一种线性三角形变网格有限元方法.其主要思路是针对空间变量采用有限元离散,对时间变量采用差分离散,但是不同时刻的有限元剖分网格可以不同.在不引入Ritz投影这一传统分析工具的情况下,得到了最优误差估计结果,使得证明过程更加简洁.给出的数值算例验证了理论分析的正确性.

In this paper,the linear triangular finite element methods with moving grids are discussed for the parabolic interface problems.The general idea is applying finite element method in space and choosing difference method with respect to the time variable,respectively,but the grids can be different when the time varies.The optimal order error estimates are obtained without introducing the Ritz projection,which is thought to be a conventional analysis tool.Thus,the analysis procedure is made to be more concise.Numerical examples are provided to verify the theoretical analysis.