Solutions to Initial Value Problems Using Finite Elements - Unconstrained Variational Formulations.

摘要

This paper presents a variational formulation which treats initial value problems and boundary problems in a unified manner. The basic ingredients of this theory are (1) adjoint variable and (2) unconstrained variations. It is an extension of the finite element-unconstrained variational formulation used previously in solving several nonconservative stability problems. The technique which makes this extension possible is described. This formulation thus enables one to adapt such numerical technique as the finite element method, which has had great success and popularity for solution of boundary value problems, for solutions of initial value problems as well. These formulations are given here for a forced vibration problem, a heat (mass) transfer problem and a wave propagation problem. Numerical calculations in conjunction with finite elements for two specific examples are obtained and compared with known exact solutions.