Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ERROR ESTIMATE OF EXTRAPOLATED DISCONTINUOUS GALERKIN APPROXIMATIONS FOR THE VISCOELASTICITY TYPE EQUATION

  • Ohm, Mi-Ray (Division of Information Systems Engineering, Dongseo University) ;
  • Lee, Hyun-Yong (Department of Mathematics, Kyungsung University) ;
  • Shin, Jun-Yong (Division of Mathematical Sciences, Pukyong National University)
  • Received : 2010.08.17
  • Accepted : 2010.11.11
  • Published : 2011.01.30
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Abstract

In this paper, we adopt discontinuous Galerkin methods with penalty terms namely symmetric interior penalty Galerkin methods, to solve nonlinear viscoelasticity type equations. We construct finite element spaces and define an appropriate projection of u and prove its optimal convergence. We construct extrapolated fully discrete discontinuous Galerkin approximations for the viscoelasticity type equation and prove ${\ell}^{\infty}(L^2)$ optimal error estimates in both spatial direction and temporal direction.

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References

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