A-POSTERIORI ERROR ESTIMATOR FOR THE CONTROL-VOLUME FINITE-ELEMENT METHOD AS APPLIED TO CONVECTION-DIFFUSION PROBLEMS

A-posteriori error estimators, as the name states, are mathematical to ols for estimating the error of numerical solutions, given the mesh an d the solution itself. The estimators can detect zones of the mesh whe re the error is expected to be high, and drive a remeshing process wit h the aim of finally smoothing the error field. In this work an a-post eriori error estimator for the control-volume finite-element method (C VFEM) is presented. The CVFEM is a nonconforming method for solving co nvection diffusion problems. The proposed estimator is shown mathemati cally to be a global upper bound of the true error, under some hypothe ses. It has been also used successfully inside an automatic adaptive l oop for two demanding benchmark cases.