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

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.