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A posteriori error estimates for a finite volume scheme applied to a nonlinear reaction-diffusion equation in population dynamics
Discrete and Continuous Dynamical Systems-Series S ( IF 1.8 ) Pub Date : 2021-05-18 , DOI: 10.3934/dcdss.2021062
Anouar El Harrak , Hatim Tayeq , Amal Bergam

This work gives a posteriori error estimates for a finite volume implicit scheme, applied to a two-time nonlinear reaction-diffusion problem in population dynamics, whose evolution processes occur at two different time scales, represented by a parameter $ \varepsilon>0 $ small enough. This work consists of building error indicators concerning time and space approximations and using them as a tool of adaptive mesh refinement in order to find approximate solutions to such models, in population dynamics, that are often hard to be handled analytically and also to be approximated numerically using the classical approach.An application of the theoretical results is provided to emphasize the efficiency of our approach compared to the classical one for a spatial inter-specific model with constant diffusivity and population growth given by a logistic law in population dynamics.

中文翻译:

应用于种群动力学中非线性反应扩散方程的有限体积方案的后验误差估计

这项工作给出了有限体积隐式方案的后验误差估计,该方案应用于种群动力学中的二次非线性反应扩散问题,其演化过程发生在两个不同的时间尺度,由参数 $ \varepsilon>0 $ small 表示足够的。这项工作包括建立关于时间和空间近似的误差指标,并将它们用作自适应网格细化的工具,以便找到此类模型的近似解,在人口动力学中,这些模型通常难以解析处理,也难以通过数值近似使用经典方法。
更新日期:2021-06-15
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