Hokkaido Mathematical Journal

LEE Ki-tak, HA Taeyoung, SHEEN Dongwoo,

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

Hokkaido Mathematical Journal, 36 (2007) pp.891-918

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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.

MSC(Primary)81U30
MSC(Secondary)35J05
Uncontrolled Keywordsdispersion relation, Helmholtz equation, finite elements