Hokkaido Mathematical Journal

Analysis of conforming and nonconforming quadrilateral finite element methods for the Helmholtz equation

Ki-tak LEE, Taeyoung HA, and Dongwoo SHEEN

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Abstract

In this paper we analyze numerical dispersion relation of some conforming and nonconforming quadrilateral finite elements. The elements employed in this analysis are the standard $Q_1$ conforming finite element, the DSSY nonconforming element [5] and the $P_1$-nonconforming quadrilateral finite element [14]. Several aspects of comparative analyses of the above three elements for two or three dimensional problems are shown.

Article information

Source
Hokkaido Math. J. Volume 36, Number 4 (2007), 891-918.

Dates
First available in Project Euclid: 3 May 2010

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1272848039

Digital Object Identifier
doi:10.14492/hokmj/1272848039

Mathematical Reviews number (MathSciNet)
MR2378297

Zentralblatt MATH identifier
1139.65074

Subjects
Primary: 81U30: Dispersion theory, dispersion relations
Secondary: 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx]

Keywords
dispersion relation Helmholtz equation finite elements

Citation

LEE, Ki-tak; HA, Taeyoung; SHEEN, Dongwoo. Analysis of conforming and nonconforming quadrilateral finite element methods for the Helmholtz equation. Hokkaido Math. J. 36 (2007), no. 4, 891--918. doi:10.14492/hokmj/1272848039. https://projecteuclid.org/euclid.hokmj/1272848039


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