The purpose of this chapter is to construct mass-lumped FEM in higher dimensions and to extend the results of the plane wave analysis carried out in 1D to 2D and 3D. We shall call the mass-lumped FEM the spectral element method, following the terminology of [83, 84]. In this first section, we shall deal with the most natural extensions of the 1D finite elements, i.e. quadrilateral elements in 2D and hexahedral elements in 3D, which can be straightforwardly derived from the 1D case by the means of Cartesian and tensor products. In order to construct spectral elements on non-regular meshes, we must first introduce the reference elements, i.e. elements defined on the unit square or the unit cube.
KeywordsQuadrature Formula Quadrature Rule Spectral Element Quadrature Point Tetrahedral Mesh
Unable to display preview. Download preview PDF.