Abstract
Most common in the fi nite element literature is the use of triangular or quadrilateral elements in 2D, or their generalisations in 3D. Until recently, finite elements in the shape of pentagons, hexagons and in general n-sided polygons have remained absent from the literature. Generalizations of the fi nite element method to arbitrary polygonal and polyhedral meshes have been the subject of increasing attention in the research community, both in computational physics and in computer graphics. In polygonal fi nite elements, the use of elements with more than four sides can provide flexibility in meshing and an improvement in solution accuracy.
In general, numerical simulations are affected by an approximation error. In order to validate the results it is necessary to provide tools to guarantee a given level of accuracy. Recovery-based error estimators in energy norm for fi nite element formulations have been proposed in the seminal work by Zienkiewicz-Zhu, and this approach has been largely extended later on by many authors. In this paper, we investigate the use of a recovery-based error indicator to perform mesh adaptivity and quality control for the polygonal fi nite element method, for smooth and singular linear elasticity.
