Jump Dominance on the Contaminant Transport Residual Error Estimator

Abstract

Considering that the transport of contaminants occurs in small advection regime,
a residual estimator is evaluated for parabolic equation that describes the phenomena of
advection-diffusion-reaction in the saturated porous medium. The correspondent numerical solution is obtained by the finite element method using the A-stable $\theta$-scheme and a Python code. The residual error estimator, associated
with the specific partial differential equation, considers its component parts, enabling analysis and contribution  comparisons from spatial and temporal discretizations. For analysis of magnitudes contributions the simulations  consideres variations in the number of elements in the initial mesh. As a result of numerical simulations, there is a dominance of the jumps residuals compared to others residuals estimates and this dominance increases with the growth of the number of elements in the computational mesh. Furthermore, the considered problem requires additional effort for the calculation of contributions associated with the $L^2$ projection of the contaminant source function on the finite element space.