Implementing the smoothness criterion in adaptive meshes

Abstract

The bending or smoothness of the vector field may be used for local error estimation in finite element analysis. However, several issues are raised regarding its implementation. Chief among them is that the field vector will often undergo a discontinuity in direction, as a result of the boundary conditions that are imposed; the ensuing error will always be sensed by the smoothness criterion and unless we stop refinement when this occurs, it will go on for ever. In this paper we give criteria for judging when to stop refinement when such enforced bending occurs and present refinement strategies which allow us to overcome the implementational difficulties of the method.