  Algebraically stabilized finite element discretizations of scalar
steady-state convection-diffusion-reaction equations often provide accurate
approximate solutions satisfying the discrete maximum principle (DMP). However,
it was observed that a deterioration of the accuracy and convergence rates may
occur for some problems if meshes without local symmetries are used. The paper
investigates these phenomena both numerically and analytically and the findings
are used to design a new algebraic stabilization called Symmetrized Monotone
Upwind-type Algebraically Stabilized (SMUAS) method. It is proved that the
SMUAS method is linearity preserving and satisfies the DMP on arbitrary
simplicial meshes. Numerical results indicate that the SMUAS method leads to
optimal convergence rates on general meshes.
