The inviscid, compressible Euler equations are generally solved in an Eulerian formulation, in which case we solve for conservation of mass, linear momentum and total energy. These equations are supplemented with constitutive laws to close the system of equations. An alternative, but hardly used approach, is to set up this model in an Lagrangian formulation, where the coordinate system moves with the flow. By doing so, the governing equations also change, \cite{Bennet,Price}. Explicitly solving for conservation of mass is no longer necessary and the convective terms are now eliminated from the system. These equations are solved with a mimetic high order spectral element. The methods will be explained and results will be presented.