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Brazil's continental dimension poses a challenge to the control of the spread of COVID-19. Due to the country specific scenario of high social and demographic heterogeneity, combined with limited testing capacity, lack of reliable data, under-reporting of cases, and restricted testing policy, the focus of this study is twofold: (i) to develop a generalized SEIRD model that implicitly takes into account the quarantine measures, and (ii) to estimate the response of the COVID-19 spread dynamics to perturbations/uncertainties. By investigating the projections of cumulative numbers of confirmed and death cases, as well as the effective reproduction number, we show that the model parameter related to social distancing measures is one of the most influential along all stages of the disease spread and the most influential after the infection peak. Due to such importance in the outcomes, different relaxation strategies of social distancing measures are investigated in order to determine which strategies are viable and less hazardous to the population. The results highlight the need of keeping social distancing policies to control the disease spread. Specifically, the considered scenario of abrupt social distancing relaxation implemented after the occurrence of the peak of positively diagnosed cases can prolong the epidemic, with a significant increase of the projected numbers of confirmed and death cases. An even worse scenario could occur if the quarantine relaxation policy is implemented before evidence of the epidemiological control, indicating the importance of the proper choice of when to start relaxing social distancing measures.

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Finite element methods are used to solve a coupled system of nonlinear partial differential equations, which models incompressible miscible displacement in porous media. Through a backward finite difference discretization in time, we define a sequentially implicit time-stepping algorithm that uncouples the system at each time-step. The Galerkin method is employed to approximate the pressure, and accurate velocity approximations are calculated via a post-processing technique involving the conservation of mass and Darcy's law. A stabilized finite element (SUPG) method is applied to the convection-diffusion equation delivering stable and accurate solutions. Error estimates with quasi-optimal rates of convergence are derived under suitable regularity hypotheses. Numerical results are presented confirming the predicted rates of convergence for the post-processing technique and illustrating the performance of the proposed methodology when applied to miscible displacements with adverse mobility ratios.