# HIGHER ORDER DISCONTINUOUS GALERKIN FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS

• 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)
• Accepted : 2014.12.05
• Published : 2014.12.25

#### Abstract

In this paper, we consider discontinuous Galerkin finite element methods with interior penalty term to approximate the solution of nonlinear parabolic problems with mixed boundary conditions. We construct the finite element spaces of the piecewise polynomials on which we define fully discrete discontinuous Galerkin approximations using the Crank-Nicolson method. To analyze the error estimates, we construct an appropriate projection which allows us to obtain the optimal order of a priori ${\ell}^{\infty}(L^2)$ error estimates of discontinuous Galerkin approximations in both spatial and temporal directions.

#### Acknowledgement

Supported by : Pukyong National University

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