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.

翻译：文件从数字和分析两个方面对这些现象进行了调查,并用研究结果设计了一种新的代数稳定方法,称为对称式单体上风式的单体振荡变平法(SMUAS),证明SMUAS方法是线性保存法,并且符合关于任意的不光滑模类的DMP, 数字结果显示SMUAS方法导致普通模类的最佳趋同率。