A simple low-degree optimal finite element scheme for the elastic transmission eigenvalue problem

Yingxia Xi; Xia Ji; Shuo Zhang

doi:10.4208/CICP.OA-2020-0260

A simple low-degree optimal finite element scheme for the elastic transmission eigenvalue problem

Yingxia Xi, Xia Ji^*, Shuo Zhang

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

The paper presents a finite element scheme for the elastic transmission eigenvalue problem written as a fourth order eigenvalue problem. The scheme uses piecewise cubic polynomials and obtains optimal convergence rate. Compared with other low-degree and nonconforming finite element schemes, the scheme inherits the continuous bilinear form which does not need extra stabilizations and is thus simple to implement.

Original language	English
Pages (from-to)	1061-1082
Number of pages	22
Journal	Communications in Computational Physics
Volume	30
Issue number	4
DOIs	https://doi.org/10.4208/CICP.OA-2020-0260
Publication status	Published - 2021

Keywords

Elastic transmission eigenvalue problem
High accuracy
Nonconforming finite element method

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10.4208/CICP.OA-2020-0260

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title = "A simple low-degree optimal finite element scheme for the elastic transmission eigenvalue problem",

abstract = "The paper presents a finite element scheme for the elastic transmission eigenvalue problem written as a fourth order eigenvalue problem. The scheme uses piecewise cubic polynomials and obtains optimal convergence rate. Compared with other low-degree and nonconforming finite element schemes, the scheme inherits the continuous bilinear form which does not need extra stabilizations and is thus simple to implement.",

keywords = "Elastic transmission eigenvalue problem, High accuracy, Nonconforming finite element method",

author = "Yingxia Xi and Xia Ji and Shuo Zhang",

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AU - Xi, Yingxia

AU - Ji, Xia

AU - Zhang, Shuo

PY - 2021

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N2 - The paper presents a finite element scheme for the elastic transmission eigenvalue problem written as a fourth order eigenvalue problem. The scheme uses piecewise cubic polynomials and obtains optimal convergence rate. Compared with other low-degree and nonconforming finite element schemes, the scheme inherits the continuous bilinear form which does not need extra stabilizations and is thus simple to implement.

AB - The paper presents a finite element scheme for the elastic transmission eigenvalue problem written as a fourth order eigenvalue problem. The scheme uses piecewise cubic polynomials and obtains optimal convergence rate. Compared with other low-degree and nonconforming finite element schemes, the scheme inherits the continuous bilinear form which does not need extra stabilizations and is thus simple to implement.

KW - Elastic transmission eigenvalue problem

KW - High accuracy

KW - Nonconforming finite element method

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U2 - 10.4208/CICP.OA-2020-0260

DO - 10.4208/CICP.OA-2020-0260

M3 - Article

AN - SCOPUS:85112378243

SN - 1815-2406

VL - 30

SP - 1061

EP - 1082

JO - Communications in Computational Physics

JF - Communications in Computational Physics

IS - 4

ER -

A simple low-degree optimal finite element scheme for the elastic transmission eigenvalue problem

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Keywords

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