A conservative spectral element method for the approximation of compressible fluid flow

A method to approximate the Euler equations is presented. The method is a m ulti-domain approximation, and a variational form of the Euler equations is found by making use of the divergence theorem. The method is similar to th at of the Discontinuous-Galerkin method of Cockburn and Shu, but the implem entation is constructed through a spectral, multi-domain approach. The meth od is introduced and is shown to be a conservative scheme. A numerical exam ple is given for the expanding flow around a point source as a comparison w ith the method proposed by Kopriva.