Abstract
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.
Highlights
Computational models that implement numerical solutions for the solute migration in saturated porous media regularly appear in scientific publications
It is appropriate to use residual error indicators to access the quality of the numerical solution obtained using the finite element method
The presentation of the indicators as a surface over the finite element mesh provides an insight into the influence of contributions on the global estimator and the magnitude of relationships between the various individual contributions
Summary
Computational models that implement numerical solutions for the solute migration in saturated porous media regularly appear in scientific publications. This problem, in general, involves description of phenomena such as retardation, reaction and sorption. Analytical solutions are not available for all types of phenomena and numerical solutions become the main tool for studying the transport of contaminants in porous media. 342 NUMERICAL RESULTS ON THE RESIDUAL ERROR INDICATOR computational schemes are not immune to errors from various sources and computational methods depends both on the choice of approximation techniques and the quality of the underlying mesh [5]. Sections presents the contaminant transport equation, finite element method with θ -scheme, the additional assumptions for residual error, residual components for each finite element, residual error estimator and residual error indicators
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