A new strategy for improving a finite element method based on explicit error estimates (Q1818491)

According to explicit error bounds in finite element methods developed by \textit{P. Ladevèze} [Comparaison de modèles de mécanique des milieux continus. Thèse d'Etat-Université Pierre et Marie Curie, Paris (1975)] and his team, this paper proposes a framework to obtain associate mathematical justifications. In this way, it uses convergence studies for primal and dual finite element methods and the relationship studied by \textit{W. Prager} and \textit{J. L. Synge} [Q. Appl. Math. 5, 241-269 (1947; Zbl 0029.23505)]. These results seem well adapted to mesh refinement algorithms. They are presented on the basic two-dimensional Poisson equations and they should be extensible to more general problems including elasticity. This paper is nicely written and does not include numerical experiments.