Purpose – In this paper, we focus on the quality of a 2D elastic finite element analysis. Design/methodology/approach – Our objective is to control the discretization parameters in order to achieve a prescribed local quality level over a dimensioning zone. The method is based on the concept of constitutive relation error. Findings – The method is illustrated through 2D test examples and shows clearly that in terms of cost, this technique provides an additional benefit compared to previous methods. Research limitations/implications – The saving would be even more significant if this mesh adaptation technique were applied in three dimensions. Indeed, in 3D problems, the computing cost is vital and, in general, it is this cost that sets the limits. Practical implications – This tool is directly usable in the design stage. Originality/value – The new tool developed guarantees a local quality level prescribed by the us