论文标题
一种代数稳定的方法，用于对流扩散反应问题，并在一般网格上具有最佳的实验收敛速率
An algebraically stabilized method for convection-diffusion-reaction problems with optimal experimental convergence rates on general meshes
论文作者
论文摘要
标量稳态对流 - 扩散反对方程的代数稳定有限元离散通常提供满足离散最大原理（DMP）的准确近似解决方案。但是，观察到，如果使用没有局部对称性的网格，可能会出现某些问题的准确性和收敛速率的恶化。该论文在数值和分析上都研究了这些现象，并将发现用于设计一种新的代数稳定化，称为对称单调单调上风型代数稳定（SMUAS）方法。事实证明，SMUAS方法是线性保留的，并满足了任意简单网格的DMP。数值结果表明，SMUA方法导致一般网格的最佳收敛速率。
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.
