NUMERICAL METHODS OF NEW MIXED FINITE ELEMENT SCHEME FOR SINGLE-PHASE COMPRESSIBLE FLOW

In this paper, a new mixed finite element scheme is given based on the less regularity of velocity for the single phase compressible flow in practice. Based on the new mixed variational formulation, we give its stable conforming finite element approximation for the P-0-P-1 pair and its stabilized conforming finite element approximation for the P-1-P-1 pair. Moreover, optimal error estimates are derived in H-1-norm and L-2-norm for the approximation of pressure and error estimate in L-2-norm for the approximation of velocity by using two methods. Finally, numerical tests confirm the theoretical results of our methods.