论文标题
在代数稳定的背景下，自适应网格用于对流扩散反应方程
Adaptive Grids in the Context of Algebraic Stabilizations for Convection-Diffusion-Reaction Equations
论文作者
论文摘要
在适应性精制的网格上研究了三个代数稳定的有限元方案，用于离散对流扩散反应方程。这些方案是具有Kuzmin限制器，具有BJK限制器的AFC方案的代数通量校正（AFC）方案，以及最近提出的单调逆风型代数稳定（MUAS）方法。两者都考虑了精制的网格的封闭，并考虑了与悬挂顶点的网格。在将这些方案应用于带有悬挂顶点的网格之前，必须进行非标准算法步骤。对于全局离散最大原理（DMP）的满意度，准确性（例如，涂抹层的涂抹）以及解决相应的非线性问题的效率，对方案进行评估。
Three algebraically stabilized finite element schemes for discretizing convection-diffusion-reaction equations are studied on adaptively refined grids. These schemes are the algebraic flux correction (AFC) scheme with Kuzmin limiter, the AFC scheme with BJK limiter, and the recently proposed Monotone Upwind-type Algebraically Stabilized (MUAS) method. Both, conforming closure of the refined grids and grids with hanging vertices are considered. A non-standard algorithmic step becomes necessary before these schemes can be applied on grids with hanging vertices. The assessment of the schemes is performed with respect to the satisfaction of the global discrete maximum principle (DMP), the accuracy, e.g., smearing of layers, and the efficiency in solving the corresponding nonlinear problems.
