Error analysis of symmetric linear/bilinear partially penalized immersed finite element methods for Helmholtz interface problems

Ruchi Guo; Tao Lin; Yanping Lin; Qiao Zhuang

doi:10.1016/j.cam.2020.113378

Error analysis of symmetric linear/bilinear partially penalized immersed finite element methods for Helmholtz interface problems

Ruchi Guo
, Tao Lin
, Yanping Lin
, Qiao Zhuang

Research output: Journal article publication › Journal article › Academic research › peer-review

7 Citations (Scopus)

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 H² regularity, the optimal error bounds for the PPIFE solutions are derived in an energy norm and the usual L² norm. A numerical example is conducted to validate the theoretical conclusions.

Original language	English
Article number	113378
Pages (from-to)	1-11
Number of pages	11
Journal	Journal of Computational and Applied Mathematics
Volume	390
DOIs	https://doi.org/10.1016/j.cam.2020.113378
Publication status	Published - Jul 2021

Keywords

Error estimates
Helmholtz type
Immersed finite element methods
Interface problems

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

More information

10.1016/j.cam.2020.113378

Cite this

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title = "Error analysis of symmetric linear/bilinear partially penalized immersed finite element methods for Helmholtz interface problems",

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 H2 regularity, the optimal error bounds for the PPIFE solutions are derived in an energy norm and the usual L2 norm. A numerical example is conducted to validate the theoretical conclusions.",

keywords = "Error estimates, Helmholtz type, Immersed finite element methods, Interface problems",

author = "Ruchi Guo and Tao Lin and Yanping Lin and Qiao Zhuang",

note = "Funding Information: Yanping Lin was partially supported by GRF B-Q56D of HKSAR and Polyu G-UA7V . Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2021",

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language = "English",

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T1 - Error analysis of symmetric linear/bilinear partially penalized immersed finite element methods for Helmholtz interface problems

AU - Guo, Ruchi

AU - Lin, Tao

AU - Lin, Yanping

AU - Zhuang, Qiao

PY - 2021/7

Y1 - 2021/7

N2 - 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 H2 regularity, the optimal error bounds for the PPIFE solutions are derived in an energy norm and the usual L2 norm. A numerical example is conducted to validate the theoretical conclusions.

AB - 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 H2 regularity, the optimal error bounds for the PPIFE solutions are derived in an energy norm and the usual L2 norm. A numerical example is conducted to validate the theoretical conclusions.

KW - Error estimates

KW - Helmholtz type

KW - Immersed finite element methods

KW - Interface problems

UR - https://www.scopus.com/pages/publications/85099613844

U2 - 10.1016/j.cam.2020.113378

DO - 10.1016/j.cam.2020.113378

M3 - Journal article

AN - SCOPUS:85099613844

SN - 0377-0427

VL - 390

SP - 1

EP - 11

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

M1 - 113378

ER -

Error analysis of symmetric linear/bilinear partially penalized immersed finite element methods for Helmholtz interface problems

Abstract

Keywords

ASJC Scopus subject areas

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