FINITE ELEMENT GALERKIN SOLUTIONS FOR THE STRONGLY DAMPED EXTENSIBLE BEAM EQUATIONS

  • Choo, S.M. (Department of Mathematics, Ulsan University) ;
  • Chung, S.K. (Department of Mathematics Education, Seoul National University) ;
  • Kannan, R. (Department of Mathematics, The University of Texas at Arlington)
  • Published : 2002.12.01

Abstract

Finite element Galerkin solutions for the strongly damped extensible beam equations are considered. The semidiscrete scheme and a fully discrete time Galerkin method are studied and the corresponding stability and error estimates are obtained. Ratios of numerical convergence are given.

Keywords

References

  1. Math. Z. v.196 Energy convergence results for strongly damped nonlinear wave equations J.D.Avrin
  2. J. Math. Anal. Appl. v.42 Initial-boundary value problems for an extensible beam J.M.Ball
  3. J. Diff. Eq. v.14 Stability theory for an extensible beam J.M.Ball
  4. Appl. Math. Lett. v.11 L²-error estimate for the strongly damped extensible beam equations S.M.Choo;S.K.Chung
  5. Appl. Math. Comp. v.112 Finite difference approximate solutions for the strongly damped extensible beam equations S.M.Choo;S.K.Chung
  6. J. Math. Appl. Anal. v.29 Free vibrations and dynamic buckling of the extensible beam R.W.Dickey
  7. Proc. Royal Soc. Edinb. v.88A Stability theory for quasi-linear wave equations with linear damping R.W.Dickey
  8. Diff. Integral Eq. v.3 Limiting behaviour of the strongly damped extensible beam equation W.E.Fitzgibbon
  9. M²AN v.23 The convergence of a Galerkin apporximation scheme for an extensible beam T.Geveci;I.Christie
  10. An analysis of the finite element method G.Strang;G.Fix
  11. J. Appl. Mech. v.17 The effect of axial force on the vibration of hinged bars S.Woionwsky-Krieger