NUMERICAL INVESTIGATION OF THE FINITE SUPERELEMENT METHOD FOR THE 3D ELASTICITY PROBLEMS

The results of numerical investigation of the Finite Superelement Method (FSEM) for the solution of 3D elasticity problems are given. A definition of FSEM is proposed, and the general theory is briefly explained. Then the variants of FSEM are considered for the model problem. Their comparative analysis is being carried out. These variants are based on the finite element interpolation techniques on superelements boundaries. FSEM and FEM efficiency comparison is presented for the model problem. Quantative error data are obtained. A certain example of a 3D elasticity problem is considered in conclusion. A notable advantage of a higher degree FSEM approximation technique is illustrated.

FEDORENKO FINITE SUPERELEMENT METHOD AS SPECIAL GALERKIN APPROXIMATION

In this work we introduce variational equation which natural Petrov‐Galerkin approximation leads to Fedorenko Finite Superelement Method (FSEM). FSEM is considered as Petrov‐Galerkin approximation of the certain problem for traces of boundary‐value problem solution at the boundaries of some subdomains (superelements). Iterative methods of solution of the same problem are well known domain decomposition methods. Some numerical results are presented.

Fedorenko Finite Superelement Method and Its Applications

This paper considers the Fedorenko Finite Superelement Method (FSEM) and some of its applications. The general idea, the main theoretical background, and the results of the numerical investigation of the method are presented using the model problem for the Laplace equation. Generalization to some other problems using the general approach suggested by the authors is also considered.