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：本文致力于设计和研究高效且精确的数值格式，用于近似模拟带有消耗效应的化学吸引模型。该模型是一个关于两个变量的非线性抛物型系统：细胞密度以及细胞所感受到的化学信号浓度。我们提出了几种有限元格式来近似该模型，详细阐述了每种格式的主要性质，如细胞守恒、能量稳定性以及近似正性。此外，我们还进行了多项数值模拟，以研究每种格式的效率，并与其他经典格式进行了比较。