Equilibration‐Based A Posteriori Error Estimates for Solid Mechanics

ABSTRACT A posteriori error estimates and the corresponding adaptive finite element methods enable the computation of solutions with a prescribed accuracy while ensuring optimal convergence rates. An important class of reliable and fully computable error estimates relies on the concept of equilibration. This contribution compares the computational efficiency of different adaptive finite element methods for linear elasticity, all relying on equilibrated stresses. A main aspect of the presented analysis is the influence of the initial mesh quality on the convergence behaviour, as initial meshes for adaptive calculations are typically coarse and therefore prone to skew cells.