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

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1976
Accession Number
ADA031410

Entities

People

  • J. J. Wu

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Civil Engineering
  • Differential Equations
  • Engineering
  • Equations
  • Finite Element Analysis
  • Heat Transfer
  • Mathematics
  • Thermal Conductivity
  • Variational Principles
  • Vibration
  • Wave Propagation
  • Waves

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Control Systems Engineering.
  • Fluid Dynamics.