论文标题
对称线性/双线性的错误分析helmholtz界面问题部分惩罚的浸入式有限元方法
Error Analysis of Symmetric Linear/Bilinear Partially Penalized Immersed Finite Element Methods for Helmholtz Interface Problems
论文作者
论文摘要
本文对Helmholtz方程的接口问题进行了对称线性/双线性部分惩罚的浸入式有限元（PPIFE）方法的错误分析。假设精确解决方案具有通常的分段$ h^2 $规律性，Ppife解决方案的最佳误差范围是在能量规范中得出的，并且通常的$ l^2 $ norm，前提是网格尺寸足够小。进行了一个数值示例来验证理论结论。
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 provided that the mesh size is sufficiently small. A numerical example is conducted to validate the theoretical conclusions.
