一类椭圆型界面问题的数值算法

Abstract

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

CLC Number:

O241.8

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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A Kind of Numerical Algorithm for Elliptic Interface Problem

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