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arXiv · 2006.10942

Error Analysis of Symmetric Linear/Bilinear Partially Penalized Immersed Finite Element Methods for Helmholtz Interface Problems

Ruchi Guo·Tao Lin·Yanping Lin·Qiao Zhuang
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Abstract

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.

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Ruchi Guo, Tao Lin, Yanping Lin, Qiao Zhuang. 2020-06-19. Error Analysis of Symmetric Linear/Bilinear Partially Penalized Immersed Finite Element Methods for Helmholtz Interface Problems. https://arxiv.org/abs/2006.10942

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