An Optimal Finite Element Mesh for Linear Elastic

This paper investigates the adaptive solution of linear elastic structural analysis problems through re-positioning of the nite element nodal points (r-renement) using an approach known as the Moving Finite Element method. After a brief introduction to the Moving Finite Element method it is proved that this technique can yield optimal nite element solutions on optimal meshes in the energy norm associated with this problem. Following this there is a discussion of the practical applications of this result in the development of adaptive software, where it is proposed that a combination of r-renement followed by local h-renement is likely to be most benecial. A small number of illustrative examples are included.