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http://dx.doi.org/10.4134/BKMS.2012.49.4.829

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.49, no.4, 2012 , pp. 829-850 More about this Journal
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.
Keywords
visoelasticity-type equation; discontinuous Galerkin methods; semidiscrete approximations; $L^2$ optimal convergence;
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