Tomás Barrios, Edwin Behrens, Rommel Bustinza:
A stabilised mixed method applied to compressible fluid flow: The stationary case
This article is concerned with a compressible fluid flow with non-homogeneous Dirichlet boundary condition. First, we reformulate the problem in its dual mixed form, and then we study its corresponding well posedness. Next, in order to circumvent the well known Babuska-Brezzi condition, we analyse a stabilised formulation of the resulting approach. Additionally, we endow the scheme with an a posteriori error estimator that is reliable and efficient. Finally, we provide numerical experiments that illustrate the performance of the corresponding adaptive algorithm and support its use in practice.