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.
Mi Ray Ohm, Hyun Young Lee, and Jun Yong Shin
Dongseo University, Kyungsung University, Pukyong National University
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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