# ERROR ESTIMATES OF SEMIDISCRETE DISCONTINUOUS GALERKIN APPROXIMATIONS FOR THE VISCOELASTICITY-TYPE EQUATION

• Published : 2012.07.31
• 31 2

#### 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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#### Acknowledgement

Supported by : Kyungsung University