In this work, we analyze the residual-based a posteriori error estimation of the multi-scale cancer invasion model, which is a system of three non-stationary reaction-diffusion equations. We present the numerical results of a study on a posteriori error control strategies for FEM approximations of the model. In this paper, we derive a residual type error estimator for the cancer invasion model and illustrate its practical performance on a series of computational tests in three-dimensional spaces. We show that the error estimator is reliable and efficient regarding the model's small perturbation parameters.

翻译：本文分析了基于残差的多尺度癌症侵袭模型的后验误差估计，该模型由三个非稳态反应扩散方程构成。我们展示了针对该模型有限元近似后验误差控制策略的数值研究成果。本文推导了癌症侵袭模型的残差型误差估计器，并通过一系列三维空间的计算测试验证其实际性能。研究表明，该误差估计器在模型小扰动参数条件下具有可靠性和高效性。