Some distributional and convergence properties of the finite element method, with applications in nonlinear elastodynamics

Variational methods of approximation have become very popular in recent years among engineers and numerical analysts. In particular, the finite element method has established itself as one of the most powerful techniques available for the approximate solution of boundary-value problems. In the present paper, we outline a number of mathematical properties of the method which are partially responsible for its success; we discuss certain error estimates and convergence results, and we describe some results obtained in applications of the method to a class of nonlinear problems in elastodynamics.