Notes on mesh optimal criteria in adaptive finite element computations

<jats:title>Abstract</jats:title><jats:p>In the paper the authors investigate the conditions of optimal mesh, and prove that the element errors in the optimal mesh should be identical for all existing elements. Also, it is shown that the correct mesh refinement formulations should be derived at an element level rather than the global level. Thus the element permissible errors need to be determined. The method to determine these permissible element errors is described.</jats:p>