AN ADAPTIVE MULTIGRID TECHNIQUE FOR 3-DIMENSIONAL ELASTICITY

A program for finite element analysis of 3D linear elasticity problems is described. The program uses quadratic hexahedral elements. The sol ution process starts on an initial coarse mesh; here error estimators are determined by the standard Babuska-Rheinboldt method and local ref inement is performed by partitioning of indicated elements, each hexah edron into eight new elements. Then the discrete problem is solved on the second mesh and the refinement process proceeds in the following w ay-on the ith mesh only the elements caused by refinement on the (i - 1)th mesh can be refined. The control of refinement is the task of the user because the dimension of the discrete problem grows very rapidly in 3D. The discrete problem is being solved by the frontal solution m ethod on the initial mesh and by a newly developed and very efficient local multigrid method on the refined meshes. The program can be succe ssfully used for solving problems with structural singularities, such as re-entrant corners and moving boundary conditions. A numerical exam ple shows that such problems are solved with the same efficiency as re gular problems.