Improvements in the Global A-Posteriori Error Estimation of the FEM and MFDM Solutions

Abstract

The present paper deals with the estimation of the solution error of the boundary value problems of mechanics science. The well-known ideas of error estimators are presented, as well as new original ones, which use the concept of the improved HO reference solution, obtained using the Meshless Finite Difference Method analysis. Such HO estimators may be applied not only in the MFDM, but also in the Finite Element Method error analysis. This issue is presented here for the first time ever. The approach is tested on chosen 2D benchmark problems. The results are very encouraging.