Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ERROR ESTIMATES OF SEMIDISCRETE DISCONTINUOUS GALERKIN APPROXIMATIONS FOR THE VISCOELASTICITY-TYPE EQUATION

  • Ohm, Mi-Ray (Division of Information Systems Engineering Dongseo University) ;
  • Lee, Hyun-Young (Department of Mathematics Kyungsung University) ;
  • Shin, Jun-Yong (Department of Applied Mathematics Pukyong National University)
  • Received : 2011.04.22
  • Published : 2012.07.31
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Abstract

In this paper, we adopt symmetric interior penalty discontinuous Galerkin (SIPG) methods to approximate the solution of nonlinear viscoelasticity-type equations. We construct finite element space which consists of piecewise continuous polynomials. We introduce an appropriate elliptic-type projection and prove its approximation properties. We construct semidiscrete discontinuous Galerkin approximations and prove the optimal convergence in $L^2$ normed space.

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References

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