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Improvements in the global a-posteriori error estimation of the FEM and MFDM solutions. (English) Zbl 1399.65261

Summary: 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.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65L10 Numerical solution of boundary value problems involving ordinary differential equations
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