Numerical results on the residual error indicator for a contaminant transport model - Martins dos Santos, João Paulo; Firmiano, Alessandro; Wendland, Edson (Trends in Computational and Applied Mathematics, 2021)
In this article, residual indicators were used to characterize the quality of the numerical solution of the advection-diffusion-reaction equation in a saturated porous medium. Both large and small advection regimes were considered. The small advection was exemplified by a problem with constant data, while non-constant data was considered for the large advection regime. In this case, residual quantities associated with the data must be incorporated into the residual estimates related to the spatial approximation and an auxiliary problem must be solved for the correct obtainment of the temporal estimates. The presentation of the residual indicators as a surface on the finite element mesh provides a detailed view of the regions that need refinement, allows to infer the effect of each estimate on the composition of the global estimator and, in addition, allows to follow the evolution of the residual surfaces as the contaminant front advances in the simulation process. In turn, the numerical values of the indicators allow to delimit the elements that will be refined, to compare the magnitude of the contributions among themselves, between different meshes and a better understanding of the composition of the global estimates.