Linear Galerkin vs mixed finite element 2D flow fields

Numerical velocity fields arising from the solution of diffusion equations by the finite element (FE) and the mixed hybrid finite element (MHFE) schemes display different behaviors. In this paper we analyze the characteristics of the two different velocity fields in terms of both accuracy and mass balance properties. General theoretical findings are mostly concerned with the asymptotic behavior of the numerical schemes, i.e. they look at properties as the mesh size tends to zero. For practical applications, it is necessary to work with a fixed mesh of given size. Thus, we attempt to characterize the numerical flow field accuracy by analyzing the resulting mass balance characteristics on a fixed mesh. The comparison is carried out by using direct local mass balance evaluations and by calculating streamlines. We detail the important differences, advantages, and disadvantages of the two approaches. In particular, we show that both FE and MH are perfectly conservative (up to the residual of the linear system solution) if proper control volumes are used. MH streamlines are admissible, i.e. numerical normal fluxes across cell interfaces are continuous. Since continuity of the normal fluxes is not guaranteed by FE, the resulting streamlines are less accurate.