Abstract
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 P0–P1 pair and its stabilized conforming finite element approximation for the P1–P1 pair. Moreover, optimal error estimates are derived in H1-norm and L2-norm for the approximation of pressure and error estimate in L2-norm for the approximation of velocity by using two methods. Finally, numerical tests confirm the theoretical results of our methods.
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