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The finite element (FE) solutions are different from the exact ones due to the presence of various error sources, such as computer round-off error, error due to discrete of the displacement field, etc. This paper uses the hand p-refinement of the finite element method for the laser butt weld problem, with the base metal is AISI 1018 steel highness 8 mm. The objective is to present estimation techniques the strain energy relative error  and evaluate its reliability through two indices: the affectivity index  and the uniformity index SD. The numerical results achieve to meet the conditions for reliability assessment. Specifically, the ,  , SD values of hrefinement, and prefinement respectively: less than 6%, 0.535667, 0.019528, and less than 4%, 0.506616, 0.103834.

THE RELIABLE ESTIMATION FOR THE LASER WELD BY THE H- AND P- REFINEMENT OF THE FINITE ELEMENT METHOD