Solving Interface Problems of the Helmholtz Equation by Immersed Finite Element Methods

doi:10.1007/s42967-019-0002-2

Abstract

Abstract: This article reports our explorations for solving interface problems of the Helmholtz equation by immersed fnite elements (IFE) on interface independent meshes. Two IFE methods are investigated:the partially penalized IFE (PPIFE) and discontinuous Galerkin IFE (DGIFE) methods. Optimal convergence rates are observed for these IFE methods once the mesh size is smaller than the optimal mesh size which is mainly dictated by the wave number. Numerical experiments also suggest that higher degree IFE methods are advantageous because of their larger optimal mesh size and higher convergence rates.

Key words: Helmholtz interface problems, Immersed fnite element(IFE)methods, Higher degree fnite element methods

CLC Number:

Tao Lin, Yanping Lin, Qiao Zhuang. Solving Interface Problems of the Helmholtz Equation by Immersed Finite Element Methods[J]. Communications on Applied Mathematics and Computation, 2019, 1(2): 187-206.

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URL: https://www.camc.shu.edu.cn/EN/10.1007/s42967-019-0002-2

https://www.camc.shu.edu.cn/EN/Y2019/V1/I2/187

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