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 Error estimates of semidiscrete discontinuous Galerkin approximations for the viscoelasticity-type equation Bull. Korean Math. Soc. 2012 Vol. 49, No. 4, 829-850 https://doi.org/10.4134/BKMS.2012.49.4.829Published online July 1, 2012 Mi Ray Ohm, Hyun Young Lee, and Jun Yong Shin Dongseo University, Kyungsung University, Pukyong National University 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 MSC numbers : 65M15, 65N30 Full-Text :