Theoretical formulations for adaptive finite element computations

<jats:title>Abstract</jats:title><jats:p>A new mesh refinement formulation for <jats:italic>h</jats:italic>‐adaptive solutions of linear elliptic problems is presented. The reliability of the methods employed for estimating errors and the convergence rate of the errors during an adaptive process are investigated by means of an asymptotic analysis method. The present adaptive mesh refinement strategy significantly improves adaptivity performance and has higher error convergence rates than those usually used. Numerical examples are shown to illustrate the efficiency of the method shown.</jats:p>