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 with respect to the small perturbation parameters in the model.

翻译：本文分析了多尺度癌症侵袭模型的基于残差的后验误差估计，该模型由三个非平稳反应扩散方程组成。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结果。本文推导了癌症侵袭模型的残差型误差估计子，并通过三维空间中的一系列计算测试说明了其实际性能。我们证明，该误差估计子相对于模型中的小扰动参数具有可靠性和有效性。