论文标题
向后的Euler阳性保存稳定方案的错误分析
Error analysis of a backward Euler positive preserving stabilized scheme for a Chemotaxis system
论文作者
论文摘要
对于两个空间维度中趋化性的凯勒 - 塞格模型，我们考虑使用局部极值减小的通量限制器来修改阳性，从而保留完全离散的方案。我们使用分段线性有限元元素在急性类型和时间的准三角测量上通过向后的Euler方法离散空间。我们假设初始数据足够小，以免对解决方案进行爆破。在适当的假设下，我们显示了完全离散的近似值的存在时间步长参数，并在细胞密度的$ l^2 $中得出误差界限，化学浓度的$ h^1 $。我们还提出了数值实验，以说明理论结果。
For a Keller-Segel model for chemotaxis in two spatial dimensions we consider a modification of a positivity preserving fully discrete scheme using a local extremum diminishing flux limiter. We discretize space using piecewise linear finite elements on an quasiuniform triangulation of acute type and time by the backward Euler method. We assume that initial data are sufficiently small in order not to have a blow-up of the solution. Under appropriate assumptions on the regularity of the exact solution and the time step parameter we show existence of the fully discrete approximation and derive error bounds in $L^2$ for the cell density and $H^1$ for the chemical concentration. We also present numerical experiments to illustrate the theoretical results.
