Reducing the Discretization Error for Global and Local Variables in Poroelasticity Problems

Resumo

This work analyzes the efficiency of the Repeated Richardson Extrapolation (RRE) to reduce the
discretization error (Eh) that results from the numerical resolution of one-dimensional poroelasticity problem. The
Finite Difference Method (FDM) was employed with second-order CDS approximation for spatial variables and
Crank-Nicolson approximation for temporal variables. The three-point Vanka smoother was used in the iterative
process. The multigrid method with W-cycles was used to accelerate the convergence of the iterative process,
which involved highly refined grids. The analyze of the results considered as local variables, the displacement and
pressure in the central point of the domain, based on localized fixed coordinate coinciding with a node point in all
grids considered; and as global variable, the average value of the variable of interest from all node values. It was
verified that employing RRE in the problems analyzed results in a significant reduction in Eh.