化学吸引-消耗模型的有限元数值格式
Finite Element numerical schemes for a chemo-attraction and consumption model
摘要：
这项工作致力于设计和研究有效和准确的数值方案，以近似一个化学吸引模型的消费效应，这是一个非线性抛物型系统的两个变量;细胞密度和浓度的化学信号，细胞感觉吸引。我们提出了几个有限元计划来近似的系统，详细介绍了每一个的主要性质，如细胞的守恒，能量稳定性和近似的积极性。此外，我们进行了几个数值模拟，研究每一个计划的效率，并比较他们与其他经典计划。
英文摘要：
This work is devoted to design and study efficient and accurate numerical schemes to approximate a chemo-attraction model with consumption effects, which is a nonlinear parabolic system for two variables; the cell density and the concentration of the chemical signal that the cell feel attracted to. We present several finite element schemes to approximate the system, detailing the main properties of each of them, such as conservation of cells, energy-stability and approximated positivity. Moreover, we carry out several numerical simulations to study the efficiency of each of the schemes and to compare them with others classical schemes.
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