An optimal finite element mesh for elastostatic structural analysis problems

This paper investigates the adaptive solution of a class of elastic structural analysis problems through re-positioning of the finite element nodal points (r-refinement) using an approach known as the moving finite element method.

Initially this adaptive method is derived for the elasticity problems of interest and it is then proved that, under certain conditions, the algorithm can yield optimal piecewise linear solutions on optimal simplicial finite element meshes. The equations of linear elasticity are then used to illustrate both the method itself and the optimality result that is derived. Finally, a number of numerical calculations are made to provide verification of the theoretical results.