Bulletin of the
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Bull. Korean Math. Soc. 2012; 49(4): 829-850

Printed July 1, 2012

https://doi.org/10.4134/BKMS.2012.49.4.829

Copyright © The Korean Mathematical Society.

Error estimates of semidiscrete discontinuous Galerkin approximations for the viscoelasticity-type equation

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

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