# A PRIORI ERROR ESTIMATES OF A DISCONTINUOUS GALERKIN METHOD FOR LINEAR SOBOLEV EQUATIONS

• Ohm, Mi-Ray (DIVISION OF INFORMATION SYSTEMS ENGINEERING, DONGSEO UNIVERSITY) ;
• Shin, Jun-Yong (DIVISION OF MATHEMATICAL SCIENCES, PUKYONG NATIONAL UNIVERSITY) ;
• Lee, Hyun-Young (DEPARTMENT OF MATHEMATICS, KYUNGSUNG UNIVERSITY)
• Accepted : 2009.06.16
• Published : 2009.09.25

#### Abstract

A discontinuous Galerkin method with interior penalty terms is presented for linear Sobolev equation. On appropriate finite element spaces, we apply a symmetric interior penalty Galerkin method to formulate semidiscrete approximate solutions. To deal with a damping term $\nabla{\cdot}({\nabla}u_t)$ included in Sobolev equations, which is the distinct character compared to parabolic differential equations, we choose special test functions. A priori error estimate for the semidiscrete time scheme is analyzed and an optimal $L^\infty(L^2)$ error estimation is derived.

#### Acknowledgement

Supported by : Kyungsung University

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