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.

翻译：这项工作致力于设计和研究高效和准确的数字方法,以接近具有消费效应的化学吸引模型,这是一种非线性抛物线系统,用于两个变量;细胞密度和细胞感觉吸引的化学信号的浓度;我们为接近这个系统提出若干有限元素方法,详细说明每个系统的主要特性,如细胞保护、能源稳定性和近似假设性;此外,我们还进行若干次数字模拟,以研究每个方案的效率,并将它们与其他典型方案进行比较。