This article presents an error analysis of the symmetric linear/bilinear partially penalized immersed finite element (PPIFE) methods for interface problems of Helmholtz equations. Under the assumption that the exact solution possesses a usual piecewise $H^2$ regularity, the optimal error bounds for the PPIFE solutions are derived in an energy norm and the usual $L^2$ norm. A numerical example is conducted to validate the theoretical conclusions.

中文翻译：

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Helmholtz界面问题的对称线性/双线性部分惩罚沉浸式有限元方法的误差分析

本文介绍了针对Helmholtz方程的界面问题的对称线性/双线性部分惩罚沉浸式有限元（PPIFE）方法的误差分析。假设精确解具有通常的分段式$H^2$ 规律性，PPIFE解的最佳误差范围是根据能量范数和通常的 ${\mathrm{大号}}^2$规范。数值例子验证了理论结论。