一类椭圆型界面问题的数值算法

摘要/Abstract

摘要：

该文基于再生核空间相关理论提出了一种一维椭圆界面问题的数值算法. 该方法通过积分${W}^{1}_{2}$空间的再生核函数, 得到了三次样条空间的一组新基, 在此基础上建立了一个破裂的三次样条空间, 然后利用最小二乘法得出了此类界面问题的近似解, 并且讨论了在$H_2$范数、$H_1$范数和$L_2$范数下的收敛阶, 最后通过几个数值算例得到了验证.

关键词: 界面问题, 再生核函数, 三次样条空间, 最小二乘法, 收敛性分析

Abstract:

In this paper, a numerical algorithm based on the theory of reproducing kernel space is proposed for the one-dimensional ellipse interface problem. This method integrates the reproducing kernel function of ${W}^{1}_{2}$ space to obtain a set of new basis in the cubic spline space, on which a broken cubic spline space is established. Then we use the least squares method to get the approximate solution of this kind of interface problem. We discussed the order of convergence under the $H_2$ norm, $H_1$ norm and $L_2$ norm. Finally, our theory is verified by several numerical example.

Key words: Interface problem, Reproducing kernel, The cubic spline space, The least squares method, Convergence analysis

中图分类号:

O241.8

于一康,牛晶. 一类椭圆型界面问题的数值算法[J]. 数学物理学报, 2023, 43(3): 883-895.

Yu Yikang,Niu Jing. A Kind of Numerical Algorithm for Elliptic Interface Problem[J]. Acta mathematica scientia,Series A, 2023, 43(3): 883-895.

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