Abstract We propose a change of variable approach and discontinuity capturing methods to ensure physical constraints for advection–reaction equations discretized by the finite element method. This change of variable confines the concentration below an upper bound in a very natural way. For the non-negativity constraint, we propose to use a discontinuity capturing method defined on the reference element that is combined with an anisotropic crosswind-dissipation operator. This discontinuity capturing cannot completely eliminate negative values but effectively minimizes their occurrence. The proposed methods are applied to different biophysical models and show a good agreement with experimental results for the FDA benchmark blood pump for a physiological red blood cell pore formation model.

中文翻译：

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具有变量变化和不连续性捕获的对流-反应方程的有限元公式

摘要 我们建议改变变量方法和不连续捕获方法，以确保对有限元方法离散化的对流-反应方程的物理约束。这种变量的变化以非常自然的方式将浓度限制在上限以下。对于非负约束，我们建议使用在参考元素上定义的不连续捕获方法，并结合各向异性侧风耗散算子。这种不连续性捕获不能完全消除负值，但可以有效地减少它们的发生。所提出的方法应用于不同的生物物理模型，并且与 FDA 基准血泵的生理红细胞孔形成模型的实验结果非常吻合。